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What is the range of the following data?23, 45, 34, 21, 89, 45, 47, 91- a)70
- b)56
- c)71
- d)69
Correct answer is option 'A'. Can you explain this answer?
What is the range of the following data?
23, 45, 34, 21, 89, 45, 47, 91
a)
70
b)
56
c)
71
d)
69
|
Vikas Kapoor answered |
Maximum and minimum value of the data 23, 45, 34, 21, 89, 45, 47, 91 are 21 and 91.
Range = 91 – 21 = 70
Range = 91 – 21 = 70
The mean deviation of the following data 14, 15, 16, 17, 13 is:- a)4
- b)2.3
- c)3
- d)1.2
Correct answer is option 'D'. Can you explain this answer?
The mean deviation of the following data 14, 15, 16, 17, 13 is:
a)
4
b)
2.3
c)
3
d)
1.2
|
|
Vikas Kapoor answered |
Here N= 5 , sigma x = 75
so mean = 15
now taking deviation from mean,( By ignoring signs)
we get sigma deviation from mean = 6
Now applying the formula of mean deviation
M.D.= SIGMA deviation from mean/ n
so M.D.= 6/5
= 1.2
so mean = 15
now taking deviation from mean,( By ignoring signs)
we get sigma deviation from mean = 6
Now applying the formula of mean deviation
M.D.= SIGMA deviation from mean/ n
so M.D.= 6/5
= 1.2
The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1,2 and 6 , the other two observations are- a)4 and 8
- b)5 and 7
- c)5 and 9
- d)4 and 9
Correct answer is option 'D'. Can you explain this answer?
The mean of 5 observations is 4.4 and their variance is 8.24. If three observations are 1,2 and 6 , the other two observations are
a)
4 and 8
b)
5 and 7
c)
5 and 9
d)
4 and 9
|
Gaurav Kumar answered |
Let the other nos. be a and b
then (x+y+1+2+6)/5 = 4.4
x + y = 13 ---------------------(1)
Variance = 8.24
41.2 = 19.88 + (x2 + 19.36 – 8.8x) + (y2 + 19.36 – 8.8y)
21.32 = x2 + y2 + 38.72 – 8.8(x + y)
x2 + y2 + 38.72 – 8.8(13) – 21.32 = 0
(using equation (1))
x2 + y2 – 97 = 0 …(2)
Squaring equation (1) both the sides,
we get (x + y)2 = (13)^2
x2 + y2 + 2xy = 169
97 + 2xy = 169
(using equation (2))
xy = 36 or x = 36/y (1)
⇒ 36/y + y = 13
y2 + 36 = 13y
y2 – 13y + 36 = 0
(y – 4)(y – 9) = 0
Either (y – 4) = 0 or (y – 9) = 0
⇒ y = 4 or y = 9
For y = 4 x = 36/y
= 36/4 = 12
For y = 9
x = 36/9
x = 4
Thus, remaining two observations are 4 and 9.
then (x+y+1+2+6)/5 = 4.4
x + y = 13 ---------------------(1)
Variance = 8.24
41.2 = 19.88 + (x2 + 19.36 – 8.8x) + (y2 + 19.36 – 8.8y)
21.32 = x2 + y2 + 38.72 – 8.8(x + y)
x2 + y2 + 38.72 – 8.8(13) – 21.32 = 0
(using equation (1))
x2 + y2 – 97 = 0 …(2)
Squaring equation (1) both the sides,
we get (x + y)2 = (13)^2
x2 + y2 + 2xy = 169
97 + 2xy = 169
(using equation (2))
xy = 36 or x = 36/y (1)
⇒ 36/y + y = 13
y2 + 36 = 13y
y2 – 13y + 36 = 0
(y – 4)(y – 9) = 0
Either (y – 4) = 0 or (y – 9) = 0
⇒ y = 4 or y = 9
For y = 4 x = 36/y
= 36/4 = 12
For y = 9
x = 36/9
x = 4
Thus, remaining two observations are 4 and 9.
A batsman scores runs in 10 innings as 38,70,48,34,42,55,63,46,54 and 44 , then the mean score is- a)4.94
- b)49.4
- c)494
- d)0.494
Correct answer is option 'B'. Can you explain this answer?
A batsman scores runs in 10 innings as 38,70,48,34,42,55,63,46,54 and 44 , then the mean score is
a)
4.94
b)
49.4
c)
494
d)
0.494
|
Mayuri Agrawal answered |
38+70+48+34+42+55+63+46+54 +44=494
494/10
=49.4
494/10
=49.4
The mean deviation about the mean for the following data:5, 6, 7, 8, 6, 9, 13, 12, 15 is:- a)1.5
- b)3.2
- c)2.89
- d)5
Correct answer is option 'C'. Can you explain this answer?
The mean deviation about the mean for the following data:
5, 6, 7, 8, 6, 9, 13, 12, 15 is:
a)
1.5
b)
3.2
c)
2.89
d)
5
|
|
Vikas Kapoor answered |
let, X =5,6,7,8,9,13,12,15.
(5+6+7+8+9+13+12+15)÷9 = 9.
and hence a = 9.
the mean deviation about the mean is summation of |X-a|÷ the total number
i.e , |X-a| = 4,3,2,1,3,0,4,3,6 and the total no. is 9.
hence summation of |X-a| = 26,
the mean deviation is 26 ÷ 9 = 2.89 ans
(5+6+7+8+9+13+12+15)÷9 = 9.
and hence a = 9.
the mean deviation about the mean is summation of |X-a|÷ the total number
i.e , |X-a| = 4,3,2,1,3,0,4,3,6 and the total no. is 9.
hence summation of |X-a| = 26,
the mean deviation is 26 ÷ 9 = 2.89 ans
For a given data, the standard deviation is 20.If 3 is added to each observation , what is the new variance of the resulting observations?- a)20
- b)23
- c)17
- d)60
Correct answer is option 'A'. Can you explain this answer?
For a given data, the standard deviation is 20.If 3 is added to each observation , what is the new variance of the resulting observations?
a)
20
b)
23
c)
17
d)
60
|
Sarita Yadav answered |
If a three, is added to each number in a set of data, the mean will be increased by 3 and the standard deviation will be unaltered (since the spread of the data will be unchanged).
Hence, variance of the new data = 20
Hence, variance of the new data = 20
If the coefficient of variation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the S.D. of the y series is- a)10.05
- b)10.1
- c)9.05
- d)9.8
Correct answer is option 'C'. Can you explain this answer?
If the coefficient of variation between x and y is 0.28, covariance between x and y is 7.6, and the variance of x is 9, then the S.D. of the y series is
a)
10.05
b)
10.1
c)
9.05
d)
9.8
|
Defence Exams answered |
Correlation coefficient = cov (x,y)/ (std deviation (x) ×std deviation (y))
Correlation coefficient = 0.28
cov (x,y) = 7.6
variance of x is 9.
=> std deviation (x) = √variance of X = √9 = 3
=> 0.28 = 7.6 / ( 3 * std deviation (y))
=> std deviation (y) = 7.6 / ( 3 * 0.28)
=> std deviation (y) = 9.05
standard deviation of Y series = 9.05
Correlation coefficient = 0.28
cov (x,y) = 7.6
variance of x is 9.
=> std deviation (x) = √variance of X = √9 = 3
=> 0.28 = 7.6 / ( 3 * std deviation (y))
=> std deviation (y) = 7.6 / ( 3 * 0.28)
=> std deviation (y) = 9.05
standard deviation of Y series = 9.05
The mean deviation about the mean for the following data 3, 7, 8, 9, 4, 6, 8, 13, 12, 10 is:- a)5
- b)3
- c)2
- d)2.4
Correct answer is option 'D'. Can you explain this answer?
The mean deviation about the mean for the following data 3, 7, 8, 9, 4, 6, 8, 13, 12, 10 is:
a)
5
b)
3
c)
2
d)
2.4
|
|
Gaurav Kumar answered |
Arrange data in ascending order,
3,4,6,7,8,8,9,10,12,13
No. of observations = 10
Median = n/2 => 10/2 = 5h observation.
5th observation is 8
Now we calculate mean deviation about median, i.e;
=> ∑∣xi−M∣/10
= {|3-8| +|4-8| +|6-8| +|7-8| +|8-8| +|8-8| +|9-8| +|10-8| +|12-8| +|13-8| }/10
= { 5 + 4 + 2 + 1 + 0 + 0 + 1 + 2 + 4 + 5}/10
= 24/10 => 2.4
3,4,6,7,8,8,9,10,12,13
No. of observations = 10
Median = n/2 => 10/2 = 5h observation.
5th observation is 8
Now we calculate mean deviation about median, i.e;
=> ∑∣xi−M∣/10
= {|3-8| +|4-8| +|6-8| +|7-8| +|8-8| +|8-8| +|9-8| +|10-8| +|12-8| +|13-8| }/10
= { 5 + 4 + 2 + 1 + 0 + 0 + 1 + 2 + 4 + 5}/10
= 24/10 => 2.4
The two lines of regression are 2x - 7y + 6 = 0 and 7x – 2y +1 = 0. What is correlation coefficient between x and y ?- a)4/49
- b)- 2/7
- c)2/7
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The two lines of regression are 2x - 7y + 6 = 0 and 7x – 2y +1 = 0. What is correlation coefficient between x and y ?
a)
4/49
b)
- 2/7
c)
2/7
d)
none of these
|
Hansa Sharma answered |
ρ = (b(xy) * b(yx))
But sign of ρρ is same as sign of b(xy), b(yx)
Therefore, ρ = 2/7
But sign of ρρ is same as sign of b(xy), b(yx)
Therefore, ρ = 2/7
The standard deviation of first 10 multiples of 4 is:- a)7
- b)8
- c)11.5
- d)14
Correct answer is option 'C'. Can you explain this answer?
The standard deviation of first 10 multiples of 4 is:
a)
7
b)
8
c)
11.5
d)
14
|
Krishna Iyer answered |
First 10 multiples of 4 are 4,8,12...40.
This is an A.P.
sum=n/2(a+l)
= 10/2(4+40)
∴ sum=220.
Mean, u=sum/n
= 220/10 = 22
D1 = 4-22 = -18
D2 = 8-22 = -16
D3 = 12-22 = -10
D4 = 16- 22 = -8
Similarly we subtract multiple of 4 by 22 upto 10 terms we get
-18, -14, -10, -8………...18
S.D. = σ2 = ∑(D2)/n
=[ (-18)2 ,(-14)2, (-10)2, (-6)2 + (-2)2 +(6)2 + (10)2 + (14)2 + (18)2]/10
Solving this, we get
σ = 11.5
This is an A.P.
sum=n/2(a+l)
= 10/2(4+40)
∴ sum=220.
Mean, u=sum/n
= 220/10 = 22
D1 = 4-22 = -18
D2 = 8-22 = -16
D3 = 12-22 = -10
D4 = 16- 22 = -8
Similarly we subtract multiple of 4 by 22 upto 10 terms we get
-18, -14, -10, -8………...18
S.D. = σ2 = ∑(D2)/n
=[ (-18)2 ,(-14)2, (-10)2, (-6)2 + (-2)2 +(6)2 + (10)2 + (14)2 + (18)2]/10
Solving this, we get
σ = 11.5
If the mean of numbers 27,31,89,107,156 is 82, then the mean of 130,126,68,50,1 is :- a)75
- b)82
- c)80
- d)157
Correct answer is option 'A'. Can you explain this answer?
If the mean of numbers 27,31,89,107,156 is 82, then the mean of 130,126,68,50,1 is :
a)
75
b)
82
c)
80
d)
157
|
Disha Bajaj answered |
To find the mean of a set of numbers, we add up all the numbers and then divide the sum by the total count of numbers.
Finding the mean of the first set of numbers:
27 + 31 + 89 + 107 + 156 = 410
The count of numbers in the first set is 5.
Mean = 410 / 5 = 82
Now, we need to find the mean of the second set of numbers using the given mean of the first set.
Finding the sum of the second set of numbers:
130 + 126 + 68 + 50 + 1 = 375
Finding the count of numbers in the second set:
There are 5 numbers in the second set.
Let's assume the mean of the second set is x.
Now, we can write the equation:
(410 + 375) / (5 + 5) = x
Simplifying the equation:
785 / 10 = x
x = 78.5
So, the mean of the second set of numbers is 78.5, which is closest to option A) 75.
Therefore, the correct answer is option A) 75.
Finding the mean of the first set of numbers:
27 + 31 + 89 + 107 + 156 = 410
The count of numbers in the first set is 5.
Mean = 410 / 5 = 82
Now, we need to find the mean of the second set of numbers using the given mean of the first set.
Finding the sum of the second set of numbers:
130 + 126 + 68 + 50 + 1 = 375
Finding the count of numbers in the second set:
There are 5 numbers in the second set.
Let's assume the mean of the second set is x.
Now, we can write the equation:
(410 + 375) / (5 + 5) = x
Simplifying the equation:
785 / 10 = x
x = 78.5
So, the mean of the second set of numbers is 78.5, which is closest to option A) 75.
Therefore, the correct answer is option A) 75.
If the mean of the squares of first n natural numbers be 11, then n is equal to- a)13
- b)5
- c)- 13/2
- d)11
Correct answer is option 'B'. Can you explain this answer?
If the mean of the squares of first n natural numbers be 11, then n is equal to
a)
13
b)
5
c)
- 13/2
d)
11
|
Learners Habitat answered |
The mean of the squares of the first n natural numbers is given by:
The sum of the squares of the first n natural numbers is:
Thus, the mean is:
We are given that the mean is 11. Therefore:
Multiply through by 6:
(n+1)(2n+1)=66
Expand:
2n2 +3n+1=66
Simplify:
2n2+3n−65=0
Solve this quadratic equation using the quadratic formula:
Here, a=2, b=3, and c=−65:
Calculate the two solutions:
Since n must be a positive integer, n=5.
The sum of the squares of the first n natural numbers is:
Thus, the mean is:
We are given that the mean is 11. Therefore:
Multiply through by 6:
(n+1)(2n+1)=66
Expand:
2n2 +3n+1=66
Simplify:
2n2+3n−65=0
Solve this quadratic equation using the quadratic formula:
Here, a=2, b=3, and c=−65:
Calculate the two solutions:
Since n must be a positive integer, n=5.
The Q.D. of the daily wages (in Rs) of 7 persons given below: 12,7,15,10,17,19,25 is- a)4.5
- b)9
- c)5
- d)14.5
Correct answer is option 'A'. Can you explain this answer?
The Q.D. of the daily wages (in Rs) of 7 persons given below: 12,7,15,10,17,19,25 is
a)
4.5
b)
9
c)
5
d)
14.5
|
Arshiya Shah answered |
Q.D. of Daily Wages of 7 Persons
To find the Q.D. (Quartile Deviation) of the daily wages of 7 persons given below: 12, 7, 15, 10, 17, 19, 25, we need to follow the steps given below:
Step 1: Arrange the data in ascending order.
7, 10, 12, 15, 17, 19, 25
Step 2: Find the median or the second quartile (Q2) of the data.
Median of the data = (n + 1)/2-th value = (7 + 1)/2-th value = 4th value
Hence, median = 15
Step 3: Find the first quartile (Q1) of the data.
Q1 = (n + 1)/4-th value = (7 + 1)/4-th value = 2nd value
Hence, Q1 = 10
Step 4: Find the third quartile (Q3) of the data.
Q3 = 3(n + 1)/4-th value = 3(7 + 1)/4-th value = 6th value
Hence, Q3 = 19
Step 5: Calculate the Quartile Deviation (Q.D.) using the formula:
Q.D. = (Q3 - Q1)/2
Substituting the values of Q1 and Q3, we get:
Q.D. = (19 - 10)/2 = 4.5
Therefore, the Q.D. of the daily wages of 7 persons given is 4.5.
Note: Quartile deviation is a measure of dispersion that gives an idea about the spread of data around the median. It is calculated as half of the difference between the third and first quartiles.
To find the Q.D. (Quartile Deviation) of the daily wages of 7 persons given below: 12, 7, 15, 10, 17, 19, 25, we need to follow the steps given below:
Step 1: Arrange the data in ascending order.
7, 10, 12, 15, 17, 19, 25
Step 2: Find the median or the second quartile (Q2) of the data.
Median of the data = (n + 1)/2-th value = (7 + 1)/2-th value = 4th value
Hence, median = 15
Step 3: Find the first quartile (Q1) of the data.
Q1 = (n + 1)/4-th value = (7 + 1)/4-th value = 2nd value
Hence, Q1 = 10
Step 4: Find the third quartile (Q3) of the data.
Q3 = 3(n + 1)/4-th value = 3(7 + 1)/4-th value = 6th value
Hence, Q3 = 19
Step 5: Calculate the Quartile Deviation (Q.D.) using the formula:
Q.D. = (Q3 - Q1)/2
Substituting the values of Q1 and Q3, we get:
Q.D. = (19 - 10)/2 = 4.5
Therefore, the Q.D. of the daily wages of 7 persons given is 4.5.
Note: Quartile deviation is a measure of dispersion that gives an idea about the spread of data around the median. It is calculated as half of the difference between the third and first quartiles.
A man tavels at a speed of 20 km/hour and then return at a speed of 30 km/hour. His average speed of the whole journey is- a)24 km/hour
- b)26 km/hour
- c)25 km/hour
- d)24.5 km/hour
Correct answer is option 'A'. Can you explain this answer?
A man tavels at a speed of 20 km/hour and then return at a speed of 30 km/hour. His average speed of the whole journey is
a)
24 km/hour
b)
26 km/hour
c)
25 km/hour
d)
24.5 km/hour
|
|
Nabanita Bajaj answered |
Solution:
The average speed of the whole journey is given by the formula:
Average speed = Total distance / Total time
Let's assume that the distance travelled by the man in one direction is 'd' km.
Therefore, the total distance travelled by the man in the whole journey is 2d km.
Let's also assume that the time taken by the man to travel 'd' km at a speed of 20 km/hour is 't1' hours.
Therefore, the time taken by the man to travel 'd' km at a speed of 30 km/hour is 't2' hours.
Using the formula:
Time = Distance / Speed
We can write:
t1 = d / 20 and t2 = d / 30
Therefore, the total time taken by the man in the whole journey is:
Total time = t1 + t2 = d / 20 + d / 30 = (3d + 2d) / (60) = 5d / 60 = d / 12 hours
Using the formula for average speed, we get:
Average speed = Total distance / Total time
= 2d / (d / 12)
= 24 km/hour
Therefore, the correct answer is option 'A' - 24 km/hour.
The average speed of the whole journey is given by the formula:
Average speed = Total distance / Total time
Let's assume that the distance travelled by the man in one direction is 'd' km.
Therefore, the total distance travelled by the man in the whole journey is 2d km.
Let's also assume that the time taken by the man to travel 'd' km at a speed of 20 km/hour is 't1' hours.
Therefore, the time taken by the man to travel 'd' km at a speed of 30 km/hour is 't2' hours.
Using the formula:
Time = Distance / Speed
We can write:
t1 = d / 20 and t2 = d / 30
Therefore, the total time taken by the man in the whole journey is:
Total time = t1 + t2 = d / 20 + d / 30 = (3d + 2d) / (60) = 5d / 60 = d / 12 hours
Using the formula for average speed, we get:
Average speed = Total distance / Total time
= 2d / (d / 12)
= 24 km/hour
Therefore, the correct answer is option 'A' - 24 km/hour.
For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?- a)15
- b)60
- c)30
- d)7.5
Correct answer is option 'B'. Can you explain this answer?
For a given data, the variance is 15. If each observation is multiplied by 2, what is the new variance of the resulting observations?
a)
15
b)
60
c)
30
d)
7.5
|
Poonam Reddy answered |
Variance = 15
New variance = 22*15
= 4*15
= 60
New variance = 22*15
= 4*15
= 60
The mean of the first n terms of the A.P. (a + d) + (a + 3d) + (a + 5d) +………..is- a)
- b)a + n2d
- c)a + nd
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
The mean of the first n terms of the A.P. (a + d) + (a + 3d) + (a + 5d) +………..is
a)
b)
a + n2d
c)
a + nd
d)
none of these
|
Manish Aggarwal answered |
The given arithmetic progression (AP) is:
(a+d),(a+3d),(a+5d),…
This sequence has a common difference of 2d.
Step 1: General term
The n-th term of this AP is given by:
Tn =a+(2n−1)d
Step 2: Sum of the first n terms
The sum of the first n terms of an AP is:
Here: First term = a+d
Last term = Tn =a+(2n−1)d
Simplify the terms:
Step 3: Mean of the first n terms
The mean of the first n terms is:
Substitute Sn:
(a+d),(a+3d),(a+5d),…
This sequence has a common difference of 2d.
Step 1: General term
The n-th term of this AP is given by:
Tn =a+(2n−1)d
Step 2: Sum of the first n terms
The sum of the first n terms of an AP is:
Here: First term = a+d
Last term = Tn =a+(2n−1)d
Simplify the terms:
Step 3: Mean of the first n terms
The mean of the first n terms is:
Substitute Sn:
The S.D. of the observations 22,26,28,20,24,30 is- a)3
- b)2.4
- c)3.42
- d)2
Correct answer is option 'C'. Can you explain this answer?
The S.D. of the observations 22,26,28,20,24,30 is
a)
3
b)
2.4
c)
3.42
d)
2
|
Lavanya Menon answered |
μ = (22 + 26 + 28 + 20 + 24 + 30)/6
= 150/6
= 25
x(i) = (xi - μ)2
x(22) = (22-25)2 = 9
x(26) = (26-25)2 = 1
x(28) = (28-25)2 = 9
x(20) = (20-25)2 = 25
x(24) = (24-25)2 = 1
x(30) = (30-25)2 = 25
(xi - μ)2 = 70
Standard deviation : [(xi - μ)2]/N
= (70/6)½
= 3.42
= 150/6
= 25
x(i) = (xi - μ)2
x(22) = (22-25)2 = 9
x(26) = (26-25)2 = 1
x(28) = (28-25)2 = 9
x(20) = (20-25)2 = 25
x(24) = (24-25)2 = 1
x(30) = (30-25)2 = 25
(xi - μ)2 = 70
Standard deviation : [(xi - μ)2]/N
= (70/6)½
= 3.42
The standard deviation for the following data:
- a)5
- b)4.21
- c)3.12
- d)None of the above
Correct answer is option 'C'. Can you explain this answer?
The standard deviation for the following data:
a)
5
b)
4.21
c)
3.12
d)
None of the above
|
|
Neha Sharma answered |
Answer: C
Solution: Variance= [summation (y^2×f) /N] -[ summation (yf) /N]^2
=(296/25) -(0/25) ^2
=11.84
standard deviation=√11.84=3.12
Solution: Variance= [summation (y^2×f) /N] -[ summation (yf) /N]^2
=(296/25) -(0/25) ^2
=11.84
standard deviation=√11.84=3.12
Coefficient of correlation between the observations (1, 6) , (2 , 5) , (3 , 4) , (4 , 3) , (5 , 2) , (6 , 1) is- a)0
- b)1
- c)-1
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Coefficient of correlation between the observations (1, 6) , (2 , 5) , (3 , 4) , (4 , 3) , (5 , 2) , (6 , 1) is
a)
0
b)
1
c)
-1
d)
none of these
|
|
Shanaya Shah answered |
Given observations: (1, 6), (2, 5), (3, 4), (4, 3), (5, 2), (6, 1)
To find the coefficient of correlation, we need to first calculate the mean and standard deviation of both the variables.
Let X be the first variable and Y be the second variable.
Calculating mean:
- Mean of X = (1+2+3+4+5+6)/6 = 3.5
- Mean of Y = (6+5+4+3+2+1)/6 = 3.5
Calculating standard deviation:
- Standard deviation of X = sqrt((1-3.5)^2 + (2-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (5-3.5)^2 + (6-3.5)^2) = 1.87
- Standard deviation of Y = sqrt((6-3.5)^2 + (5-3.5)^2 + (4-3.5)^2 + (3-3.5)^2 + (2-3.5)^2 + (1-3.5)^2) = 1.87
Calculating the coefficient of correlation using the formula:
r = Σ((Xi - X̄)(Yi - Ȳ))/sqrt(Σ(Xi - X̄)^2 * Σ(Yi - Ȳ)^2)
Substituting the values,
r = ((-2.5)*4.5 + (-1.5)*2.5 + (-0.5)*0.5 + 0.5*2.5 + 1.5*4.5 + 2.5*6.5)/(1.87^2 * 1.87^2 * 6)
r = -1
Therefore, the coefficient of correlation between the given observations is -1, which indicates a perfect negative correlation.
To find the coefficient of correlation, we need to first calculate the mean and standard deviation of both the variables.
Let X be the first variable and Y be the second variable.
Calculating mean:
- Mean of X = (1+2+3+4+5+6)/6 = 3.5
- Mean of Y = (6+5+4+3+2+1)/6 = 3.5
Calculating standard deviation:
- Standard deviation of X = sqrt((1-3.5)^2 + (2-3.5)^2 + (3-3.5)^2 + (4-3.5)^2 + (5-3.5)^2 + (6-3.5)^2) = 1.87
- Standard deviation of Y = sqrt((6-3.5)^2 + (5-3.5)^2 + (4-3.5)^2 + (3-3.5)^2 + (2-3.5)^2 + (1-3.5)^2) = 1.87
Calculating the coefficient of correlation using the formula:
r = Σ((Xi - X̄)(Yi - Ȳ))/sqrt(Σ(Xi - X̄)^2 * Σ(Yi - Ȳ)^2)
Substituting the values,
r = ((-2.5)*4.5 + (-1.5)*2.5 + (-0.5)*0.5 + 0.5*2.5 + 1.5*4.5 + 2.5*6.5)/(1.87^2 * 1.87^2 * 6)
r = -1
Therefore, the coefficient of correlation between the given observations is -1, which indicates a perfect negative correlation.
Mean of the squares of the deviations from mean is called the:- a)Mode
- b)Standard deviation
- c)Variance
- d)Quartile deviation
Correct answer is option 'C'. Can you explain this answer?
Mean of the squares of the deviations from mean is called the:
a)
Mode
b)
Standard deviation
c)
Variance
d)
Quartile deviation
|
Jyoti Kapoor answered |
Squared deviations from the mean Squared deviations from the mean (SDM) are involved in various calculations. In probability theory and statistics, the definition of variance is either the expected value of the SDM (when considering a theoretical distribution) or its average value (for actual experimental data).
A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 , then the mean deviation is- a)6.4
- b)9.6
- c)10.6
- d)8.6
Correct answer is option 'D'. Can you explain this answer?
A batsman scores runs in 10 innings 38,70,48,34,42,55,63,46,54 and 44 , then the mean deviation is
a)
6.4
b)
9.6
c)
10.6
d)
8.6
|
|
Jyoti Sengupta answered |
Arranging the given data in ascending order,
we have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, Median M = (46+48)/2
=47
(∵ n = 10, median is the mean of 5th and 6th items)
∴ Mean deviation = ∑|xi−M|/n
=∑|xi−47|/10
= (13+9+5+3+1+1+7+8+16+23)/10
=8.6
we have 34, 38, 42, 44, 46, 48, 54, 55, 63, 70
Here, Median M = (46+48)/2
=47
(∵ n = 10, median is the mean of 5th and 6th items)
∴ Mean deviation = ∑|xi−M|/n
=∑|xi−47|/10
= (13+9+5+3+1+1+7+8+16+23)/10
=8.6
The H.M. of 4,8,16 is- a)6.7
- b)7.8
- c)6.85
- d)6.4
Correct answer is option 'C'. Can you explain this answer?
The H.M. of 4,8,16 is
a)
6.7
b)
7.8
c)
6.85
d)
6.4
|
|
Vivek answered |
HM = 3*(1/4 + 1/8 + 1/16)-¹
= 6.85
KEY POINT →→ HM of n terms = n*[1/a + 1/b + (upto
n terms) ]-¹
If in moderately asymmetrical distribution mode and mean of the data are 6 μ and 9 μ respectively, then median is- a)8 μ
- b)6 μ
- c)5 μ
- d)7 μ
Correct answer is option 'A'. Can you explain this answer?
If in moderately asymmetrical distribution mode and mean of the data are 6 μ and 9 μ respectively, then median is
a)
8 μ
b)
6 μ
c)
5 μ
d)
7 μ
|
|
Ananya Das answered |
Median = [mode + 2(mean)]/3
= [6μ+2(9μ)]/3
= 24μ/3
= 8μ
= [6μ+2(9μ)]/3
= 24μ/3
= 8μ
The Mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0.- a)2
- b)5
- c)0
- d)6
Correct answer is option 'D'. Can you explain this answer?
The Mode of the following items is 0,1,6,7,2,3,7,6,6,2,6,0,5,6,0.
a)
2
b)
5
c)
0
d)
6
|
|
Manish Aggarwal answered |
To find the mode, we count how many times each number appears:
- 0 appears 3 times.
- 1 appears 1 time.
- 6 appears 5 times.
- 7 appears 2 times.
- 2 appears 2 times.
- 3 appears 1 time.
- 5 appears 1 time.
Since 6 occurs the most frequently (5 times), the mode is 6.
Thus, the correct answer is:
D: 6
If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρρsatisfies.- a)ρ = 0
- b)ρ > 0
- c)ρ = 1 or −1
- d)ρ < 0
Correct answer is option 'C'. Can you explain this answer?
If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient ρρsatisfies.
a)
ρ = 0
b)
ρ > 0
c)
ρ = 1 or −1
d)
ρ < 0
|
|
Aman Chauhan answered |
If the two lines of regression of a bivariate distribution coincide, then the correlation coefficient is +1 or -1, indicating a perfect linear relationship between the two variables.
The two lines of regression are x + 4y = 3 and 3x +y = 15. value of x for y = 3 is- a)- 4
- b)4
- c)- 9
- d)none of these
Correct answer is option 'B'. Can you explain this answer?
The two lines of regression are x + 4y = 3 and 3x +y = 15. value of x for y = 3 is
a)
- 4
b)
4
c)
- 9
d)
none of these
|
Pragati Nair answered |
We have x + 4y = 3 and 3x + y = 15 as the lines of regression of y on x and x on y respectively.
Therefore, for y = 3 the required line is x on y
so put y= 3 in 3x + y = 15
we get, x = 4
Therefore, for y = 3 the required line is x on y
so put y= 3 in 3x + y = 15
we get, x = 4
If the median = (mode + 2 mean) μ, then μ is equal to- a)3
- b)1/3
- c)2/3
- d)2
Correct answer is option 'B'. Can you explain this answer?
If the median = (mode + 2 mean) μ, then μ is equal to
a)
3
b)
1/3
c)
2/3
d)
2
|
|
Muskaan Singh answered |
If the median equals the mode plus twice the mean, we can express this relationship mathematically as:
Median = Mode + 2 * Mean
Median = Mode + 2 * Mean
If the mean of the first n odd natural numbers be n itself, then n is equal to- a)3
- b)any natural number
- c)2
- d)1
Correct answer is option 'B'. Can you explain this answer?
If the mean of the first n odd natural numbers be n itself, then n is equal to
a)
3
b)
any natural number
c)
2
d)
1
|
Tarun Kaushik answered |
The first n odd natural numbers are 1,3,5,…,(2n−1). The mean of these numbers is calculated as:
The sum of the first n odd natural numbers is:
Sum=n2
So, the mean becomes:
We are given that the mean is equal to n itself. This equality holds true for any natural number n.
The sum of the first n odd natural numbers is:
Sum=n2
So, the mean becomes:
We are given that the mean is equal to n itself. This equality holds true for any natural number n.
For a normal distribution, we have- a)mean = median = mode
- b)mean = mode
- c)median = mode
- d)mean = median
Correct answer is option 'A'. Can you explain this answer?
For a normal distribution, we have
a)
mean = median = mode
b)
mean = mode
c)
median = mode
d)
mean = median
|
Nipuns Institute answered |
For a normal distribution, the following property holds:
Mean=Median=Mode
This is because a normal distribution is symmetric about its center, and the mean, median, and mode all lie at the same central point.
Mean=Median=Mode
This is because a normal distribution is symmetric about its center, and the mean, median, and mode all lie at the same central point.
The mean weight of a group of 10 items is 28 and that of another group of n items is 35.The mean of combined group of 10 + n items is found to be 30. The value of n is- a)12
- b)10
- c)4
- d)2
Correct answer is option 'C'. Can you explain this answer?
The mean weight of a group of 10 items is 28 and that of another group of n items is 35.The mean of combined group of 10 + n items is found to be 30. The value of n is
a)
12
b)
10
c)
4
d)
2
|
Bhavana Shah answered |
Given:
- Mean weight of 10 items = 28
- Mean weight of n items = 35
- Mean weight of combined group of 10+n items = 30
To find: Value of n
Solution:
Let's start by using the formula for the mean of a group of items:
Mean = (Sum of all items) / (Number of items)
We can use this formula for each of the three groups mentioned in the question:
Group 1 (10 items):
Mean = 28
Number of items = 10
Sum of all items = 28 * 10 = 280
Group 2 (n items):
Mean = 35
Number of items = n
Sum of all items = 35n
Combined group (10+n items):
Mean = 30
Number of items = 10 + n
Sum of all items = 30 * (10 + n) = 300 + 30n
Now we can use the fact that the combined group consists of items from Group 1 and Group 2:
Sum of all items in combined group = Sum of all items in Group 1 + Sum of all items in Group 2
300 + 30n = 280 + 35n
Solving for n:
30n - 35n = 280 - 300
-5n = -20
n = 4
Therefore, the value of n is 4, which is option (c).
- Mean weight of 10 items = 28
- Mean weight of n items = 35
- Mean weight of combined group of 10+n items = 30
To find: Value of n
Solution:
Let's start by using the formula for the mean of a group of items:
Mean = (Sum of all items) / (Number of items)
We can use this formula for each of the three groups mentioned in the question:
Group 1 (10 items):
Mean = 28
Number of items = 10
Sum of all items = 28 * 10 = 280
Group 2 (n items):
Mean = 35
Number of items = n
Sum of all items = 35n
Combined group (10+n items):
Mean = 30
Number of items = 10 + n
Sum of all items = 30 * (10 + n) = 300 + 30n
Now we can use the fact that the combined group consists of items from Group 1 and Group 2:
Sum of all items in combined group = Sum of all items in Group 1 + Sum of all items in Group 2
300 + 30n = 280 + 35n
Solving for n:
30n - 35n = 280 - 300
-5n = -20
n = 4
Therefore, the value of n is 4, which is option (c).
Least square lines of regression give best possible estimates, when ρ(X,Y) is equal to- a)- 1 or 1
- b)less than 1
- c)greater than -1
- d)1/ 2
Correct answer is option 'A'. Can you explain this answer?
Least square lines of regression give best possible estimates, when ρ(X,Y) is equal to
a)
- 1 or 1
b)
less than 1
c)
greater than -1
d)
1/ 2
|
Krithika Deshpande answered |
The relationship between the variables is linear and the data points are normally distributed around the regression line.
If the two lines of regression are at right angles, then ρ(X,Y) is equal to- a)- 1
- b)0
- c)1
- d)1 or - 1
Correct answer is option 'B'. Can you explain this answer?
If the two lines of regression are at right angles, then ρ(X,Y) is equal to
a)
- 1
b)
0
c)
1
d)
1 or - 1
|
|
Nabanita Bajaj answered |
Understanding Regression Lines and Correlation
When two lines of regression are at right angles, it provides critical information about the relationship between the variables X and Y.
Correlation Coefficient (ρ)
- The correlation coefficient (ρ) quantifies the degree of linear relationship between two variables.
- Its value ranges from -1 to +1:
- ρ = 1 indicates a perfect positive correlation.
- ρ = -1 indicates a perfect negative correlation.
- ρ = 0 indicates no correlation.
Right Angles and Independence
- Lines of regression are perpendicular (at right angles) when the product of their slopes equals -1.
- This condition signifies that changes in one variable do not predict changes in the other, indicating independence.
Conclusion: The Value of ρ
- When the lines of regression are at right angles, it implies that:
- There is no linear relationship between X and Y.
- Thus, ρ must equal 0.
This leads us to conclude that the correct answer to the question is option 'B', which states that ρ(X,Y) is equal to 0.
When two lines of regression are at right angles, it provides critical information about the relationship between the variables X and Y.
Correlation Coefficient (ρ)
- The correlation coefficient (ρ) quantifies the degree of linear relationship between two variables.
- Its value ranges from -1 to +1:
- ρ = 1 indicates a perfect positive correlation.
- ρ = -1 indicates a perfect negative correlation.
- ρ = 0 indicates no correlation.
Right Angles and Independence
- Lines of regression are perpendicular (at right angles) when the product of their slopes equals -1.
- This condition signifies that changes in one variable do not predict changes in the other, indicating independence.
Conclusion: The Value of ρ
- When the lines of regression are at right angles, it implies that:
- There is no linear relationship between X and Y.
- Thus, ρ must equal 0.
This leads us to conclude that the correct answer to the question is option 'B', which states that ρ(X,Y) is equal to 0.
The statistical method which helps us to estimate or predict the unknown value of one variable from the known value of the related variable is called- a)correlation
- b)regression
- c)scatter diagram
- d)dispersion
Correct answer is option 'B'. Can you explain this answer?
The statistical method which helps us to estimate or predict the unknown value of one variable from the known value of the related variable is called
a)
correlation
b)
regression
c)
scatter diagram
d)
dispersion
|
|
Disha Bajaj answered |
Regression is the statistical method that helps us estimate or predict the unknown value of one variable from the known value of a related variable. It is widely used in various fields such as economics, finance, social sciences, and engineering to analyze and model the relationship between variables.
Explanation:
Regression involves finding a mathematical equation that best describes the relationship between two or more variables. It is based on the concept of a dependent variable and one or more independent variables. The dependent variable is the variable that we want to estimate or predict, while the independent variables are the known values that we use to make the estimation or prediction.
Key Points:
- Regression analysis helps us understand the relationship between variables and enables us to make predictions or estimations based on this relationship.
- It is often used to examine how changes in one variable are associated with changes in another variable.
- The most common type of regression analysis is simple linear regression, which assumes a linear relationship between the variables.
- In simple linear regression, the equation takes the form of Y = a + bX, where Y is the dependent variable, X is the independent variable, a is the intercept, and b is the slope.
- The intercept represents the value of the dependent variable when the independent variable is zero, while the slope represents the change in the dependent variable for a one-unit increase in the independent variable.
- Regression analysis can also be extended to multiple regression, where there are more than one independent variables.
- Multiple regression allows us to account for the effects of multiple variables on the dependent variable and can provide more accurate predictions.
- Regression analysis is typically performed using statistical software, which calculates the coefficients of the equation and provides measures of the goodness of fit and statistical significance.
In conclusion, regression is a powerful statistical method that allows us to estimate or predict unknown values based on known values of related variables. It is widely used in various fields to analyze and model relationships between variables, providing valuable insights and predictions.
Explanation:
Regression involves finding a mathematical equation that best describes the relationship between two or more variables. It is based on the concept of a dependent variable and one or more independent variables. The dependent variable is the variable that we want to estimate or predict, while the independent variables are the known values that we use to make the estimation or prediction.
Key Points:
- Regression analysis helps us understand the relationship between variables and enables us to make predictions or estimations based on this relationship.
- It is often used to examine how changes in one variable are associated with changes in another variable.
- The most common type of regression analysis is simple linear regression, which assumes a linear relationship between the variables.
- In simple linear regression, the equation takes the form of Y = a + bX, where Y is the dependent variable, X is the independent variable, a is the intercept, and b is the slope.
- The intercept represents the value of the dependent variable when the independent variable is zero, while the slope represents the change in the dependent variable for a one-unit increase in the independent variable.
- Regression analysis can also be extended to multiple regression, where there are more than one independent variables.
- Multiple regression allows us to account for the effects of multiple variables on the dependent variable and can provide more accurate predictions.
- Regression analysis is typically performed using statistical software, which calculates the coefficients of the equation and provides measures of the goodness of fit and statistical significance.
In conclusion, regression is a powerful statistical method that allows us to estimate or predict unknown values based on known values of related variables. It is widely used in various fields to analyze and model relationships between variables, providing valuable insights and predictions.
If x and y are related as y – 4x = 3, then the nature of correlation between x and y is- a)perfect negative
- b)no correlation
- c)perfect positive
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If x and y are related as y – 4x = 3, then the nature of correlation between x and y is
a)
perfect negative
b)
no correlation
c)
perfect positive
d)
none of these
|
|
Rohan Singh answered |
Positive correlation is a relationship between two variables in which both variables move in tandem. A positive correlation exists when one variable decreases as the other variable decreases, or one variable increases while the other increases.
For a symmetrical distribution Q1 = 20 and Q3. = 40. The median of the data is- a)10
- b)40
- c)20
- d)30
Correct answer is option 'D'. Can you explain this answer?
For a symmetrical distribution Q1 = 20 and Q3. = 40. The median of the data is
a)
10
b)
40
c)
20
d)
30
|
|
Gauri Rane answered |
Understanding Symmetrical Distribution
In a symmetrical distribution, the data is evenly distributed around its central point, which is the median. The key characteristics of this distribution are:
- The mean, median, and mode are all equal.
- The quartiles (Q1 and Q3) divide the data into segments.
Given Values
- Q1 (First Quartile) = 20
- Q3 (Third Quartile) = 40
In a symmetrical distribution, the median can be found using the following relationship between quartiles:
Median Calculation
- The median lies exactly halfway between Q1 and Q3 in a symmetrical distribution.
- To find the median, you can use the formula:
Median = (Q1 + Q3) / 2
Substituting the given values:
- Median = (20 + 40) / 2
- Median = 60 / 2
- Median = 30
Conclusion
Thus, the median of the data is 30, which corresponds to option 'D'. This result aligns with the principles of symmetrical distributions, confirming that the data is balanced around this central point.
In a symmetrical distribution, the data is evenly distributed around its central point, which is the median. The key characteristics of this distribution are:
- The mean, median, and mode are all equal.
- The quartiles (Q1 and Q3) divide the data into segments.
Given Values
- Q1 (First Quartile) = 20
- Q3 (Third Quartile) = 40
In a symmetrical distribution, the median can be found using the following relationship between quartiles:
Median Calculation
- The median lies exactly halfway between Q1 and Q3 in a symmetrical distribution.
- To find the median, you can use the formula:
Median = (Q1 + Q3) / 2
Substituting the given values:
- Median = (20 + 40) / 2
- Median = 60 / 2
- Median = 30
Conclusion
Thus, the median of the data is 30, which corresponds to option 'D'. This result aligns with the principles of symmetrical distributions, confirming that the data is balanced around this central point.
For a moderately skewed distribution, quartile deviation and the standard deviation are related by- a)S.D. = 3/2 Q.D.
- b)S.D = 3/4 Q.D.
- c)S.D. = 4/3 Q.D.
- d)S.D. = 2/3 Q.D.
Correct answer is option 'A'. Can you explain this answer?
For a moderately skewed distribution, quartile deviation and the standard deviation are related by
a)
S.D. = 3/2 Q.D.
b)
S.D = 3/4 Q.D.
c)
S.D. = 4/3 Q.D.
d)
S.D. = 2/3 Q.D.
|
|
Sushant Chaudhary answered |
The relationship between the mean, quartile and the standard deviation are as follows:
Mean Deviation is the mean of all the absolute deviations of a set of data.
Quartile deviation is the difference between “first and third quartiles” in any distribution.
Standard deviation measures the “dispersion of the data set” that is relative to its mean.
Mean Deviation = 4/5 × Quartile deviation
Standard Deviation = 3/2 × Quartile deviation
Mean Deviation is the mean of all the absolute deviations of a set of data.
Quartile deviation is the difference between “first and third quartiles” in any distribution.
Standard deviation measures the “dispersion of the data set” that is relative to its mean.
Mean Deviation = 4/5 × Quartile deviation
Standard Deviation = 3/2 × Quartile deviation
Mean deviation from the mean for the observations – 1, 0 ,4 is- a)2/3
- b)3/2
- c)2
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
Mean deviation from the mean for the observations – 1, 0 ,4 is
a)
2/3
b)
3/2
c)
2
d)
none of these
|
|
Bhargavi Bose answered |
To calculate the mean deviation from the mean for a set of observations, follow these steps:
1. Calculate the mean of the observations by adding all the values together and dividing by the total number of observations.
2. Subtract the mean from each individual observation to find the deviation from the mean.
3. Take the absolute value of each deviation to ensure that negative values do not cancel out positive values.
4. Add up all the absolute deviations.
5. Divide the sum of the absolute deviations by the total number of observations to find the mean deviation from the mean.
Here is an example:
Observations: 5, 7, 9, 12, 15
1. Mean = (5 + 7 + 9 + 12 + 15) / 5 = 9.6
2. Deviations from the mean: -4.6, -2.6, -0.6, 2.4, 5.4
3. Absolute deviations: 4.6, 2.6, 0.6, 2.4, 5.4
4. Sum of absolute deviations: 15.6
5. Mean deviation from the mean = 15.6 / 5 = 3.12
Therefore, the mean deviation from the mean for these observations is 3.12.
1. Calculate the mean of the observations by adding all the values together and dividing by the total number of observations.
2. Subtract the mean from each individual observation to find the deviation from the mean.
3. Take the absolute value of each deviation to ensure that negative values do not cancel out positive values.
4. Add up all the absolute deviations.
5. Divide the sum of the absolute deviations by the total number of observations to find the mean deviation from the mean.
Here is an example:
Observations: 5, 7, 9, 12, 15
1. Mean = (5 + 7 + 9 + 12 + 15) / 5 = 9.6
2. Deviations from the mean: -4.6, -2.6, -0.6, 2.4, 5.4
3. Absolute deviations: 4.6, 2.6, 0.6, 2.4, 5.4
4. Sum of absolute deviations: 15.6
5. Mean deviation from the mean = 15.6 / 5 = 3.12
Therefore, the mean deviation from the mean for these observations is 3.12.
Which one of the following average is most affected of extreme observations ?- a)Median
- b)Mode
- c)G.M.
- d)A. M.
Correct answer is option 'D'. Can you explain this answer?
Which one of the following average is most affected of extreme observations ?
a)
Median
b)
Mode
c)
G.M.
d)
A. M.
|
|
Mansi Menon answered |
Introduction:
The question asks us to identify which average is most affected by extreme observations. We have four options to choose from: Median, Mode, Geometric Mean (G.M.), and Arithmetic Mean (A.M.).
Explanation:
To determine which average is most affected by extreme observations, we need to understand how each average is calculated and how extreme observations can impact them.
Median:
The median is the middle value in a set of data when the data is arranged in ascending or descending order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.
Extreme observations have minimal impact on the median. Even if there are extremely high or low values, the median will remain relatively unchanged as long as they are not in the middle position. Therefore, we can eliminate option (a) Median as the correct answer.
Mode:
The mode is the value or values that appear most frequently in a set of data. Extreme observations have no impact on the mode unless they are the most frequently occurring values. Since extreme observations do not necessarily affect the mode, we can eliminate option (b) Mode as the correct answer.
Geometric Mean (G.M.):
The geometric mean is the nth root of the product of n numbers. Extreme observations can significantly affect the geometric mean, especially if they are large or small values. The product of extreme values will dominate the overall calculation, leading to a higher or lower geometric mean. Therefore, option (c) G.M. is also eliminated as the correct answer.
Arithmetic Mean (A.M.):
The arithmetic mean is calculated by summing all the values in a set of data and dividing by the number of observations. Extreme observations can have a significant impact on the arithmetic mean, especially if they are large or small values. Adding extreme values to the sum will increase or decrease the overall calculation, leading to a higher or lower arithmetic mean. Therefore, option (d) A.M. is the correct answer.
Conclusion:
After analyzing the impact of extreme observations on each average, we can conclude that the arithmetic mean (A.M.) is the average that is most affected by extreme observations. Extreme values have minimal impact on the median and mode, but they can significantly affect the geometric mean and arithmetic mean.
The question asks us to identify which average is most affected by extreme observations. We have four options to choose from: Median, Mode, Geometric Mean (G.M.), and Arithmetic Mean (A.M.).
Explanation:
To determine which average is most affected by extreme observations, we need to understand how each average is calculated and how extreme observations can impact them.
Median:
The median is the middle value in a set of data when the data is arranged in ascending or descending order. If there is an odd number of observations, the median is the middle value. If there is an even number of observations, the median is the average of the two middle values.
Extreme observations have minimal impact on the median. Even if there are extremely high or low values, the median will remain relatively unchanged as long as they are not in the middle position. Therefore, we can eliminate option (a) Median as the correct answer.
Mode:
The mode is the value or values that appear most frequently in a set of data. Extreme observations have no impact on the mode unless they are the most frequently occurring values. Since extreme observations do not necessarily affect the mode, we can eliminate option (b) Mode as the correct answer.
Geometric Mean (G.M.):
The geometric mean is the nth root of the product of n numbers. Extreme observations can significantly affect the geometric mean, especially if they are large or small values. The product of extreme values will dominate the overall calculation, leading to a higher or lower geometric mean. Therefore, option (c) G.M. is also eliminated as the correct answer.
Arithmetic Mean (A.M.):
The arithmetic mean is calculated by summing all the values in a set of data and dividing by the number of observations. Extreme observations can have a significant impact on the arithmetic mean, especially if they are large or small values. Adding extreme values to the sum will increase or decrease the overall calculation, leading to a higher or lower arithmetic mean. Therefore, option (d) A.M. is the correct answer.
Conclusion:
After analyzing the impact of extreme observations on each average, we can conclude that the arithmetic mean (A.M.) is the average that is most affected by extreme observations. Extreme values have minimal impact on the median and mode, but they can significantly affect the geometric mean and arithmetic mean.
Quartile deviation is nearly equal to- a)3/2 σ
- b)2 σ
- c)2/3 σ
- d)3 σ
Correct answer is option 'C'. Can you explain this answer?
Quartile deviation is nearly equal to
a)
3/2 σ
b)
2 σ
c)
2/3 σ
d)
3 σ
|
EduRev JEE answered |
The quartile deviation (also called the semi-interquartile range) is approximately related to the standard deviation (σ) by the formula:
This relationship holds in cases where the data follows a normal distribution, as the quartile deviation is a measure of spread that focuses on the interquartile range.
This relationship holds in cases where the data follows a normal distribution, as the quartile deviation is a measure of spread that focuses on the interquartile range.
In a group of students, mean weight of boys is 80 kg and mean weight of girls is 50kg.If the mean weight of all the students taken together is 60kg, then the ratio of the number of boys to that of the girls is- a)2 : 1
- b)3 : 2
- c)1 : 2
- d)2 : 3
Correct answer is option 'C'. Can you explain this answer?
In a group of students, mean weight of boys is 80 kg and mean weight of girls is 50kg.If the mean weight of all the students taken together is 60kg, then the ratio of the number of boys to that of the girls is
a)
2 : 1
b)
3 : 2
c)
1 : 2
d)
2 : 3
|
Tanvi Roy answered |
Understanding the Problem
In this problem, we have the mean weights of boys and girls, and we need to find the ratio of the number of boys to the number of girls based on the overall mean weight of the group.
Given Data
- Mean weight of boys = 80 kg
- Mean weight of girls = 50 kg
- Overall mean weight of students = 60 kg
Let’s Define Variables
- Let the number of boys = b
- Let the number of girls = g
Calculating Total Weights
- Total weight of boys = 80b
- Total weight of girls = 50g
Overall Mean Weight Formula
The overall mean weight is calculated as:
Overall Mean = (Total weight of boys + Total weight of girls) / (Number of boys + Number of girls)
Substituting the known values, we have:
60 = (80b + 50g) / (b + g)
Cross-Multiplying
60(b + g) = 80b + 50g
This simplifies to:
60b + 60g = 80b + 50g
Rearranging the Equation
By moving the terms involving b and g to one side, we get:
60g - 50g = 80b - 60b
This further simplifies to:
10g = 20b
Finding the Ratio
From the equation, we can derive the ratio:
g/b = 20/10 = 2
This means:
b/g = 1/2
Thus, the ratio of boys to girls is:
Final Ratio
The ratio of the number of boys to the number of girls is 1:2.
Therefore, the correct answer is option 'C'.
In this problem, we have the mean weights of boys and girls, and we need to find the ratio of the number of boys to the number of girls based on the overall mean weight of the group.
Given Data
- Mean weight of boys = 80 kg
- Mean weight of girls = 50 kg
- Overall mean weight of students = 60 kg
Let’s Define Variables
- Let the number of boys = b
- Let the number of girls = g
Calculating Total Weights
- Total weight of boys = 80b
- Total weight of girls = 50g
Overall Mean Weight Formula
The overall mean weight is calculated as:
Overall Mean = (Total weight of boys + Total weight of girls) / (Number of boys + Number of girls)
Substituting the known values, we have:
60 = (80b + 50g) / (b + g)
Cross-Multiplying
60(b + g) = 80b + 50g
This simplifies to:
60b + 60g = 80b + 50g
Rearranging the Equation
By moving the terms involving b and g to one side, we get:
60g - 50g = 80b - 60b
This further simplifies to:
10g = 20b
Finding the Ratio
From the equation, we can derive the ratio:
g/b = 20/10 = 2
This means:
b/g = 1/2
Thus, the ratio of boys to girls is:
Final Ratio
The ratio of the number of boys to the number of girls is 1:2.
Therefore, the correct answer is option 'C'.
If the mean of 3,4,x,7,10, is 6, then the value of x is- a)7
- b)5
- c)4
- d)6
Correct answer is option 'D'. Can you explain this answer?
If the mean of 3,4,x,7,10, is 6, then the value of x is
a)
7
b)
5
c)
4
d)
6
|
|
Tanishq Singh answered |
Question:
If the mean of 3, 4, x, 7, 10 is 6, then the value of x is
Answer:
To find the value of x, we need to use the formula for the mean, which is the sum of all the numbers divided by the total number of numbers.
The formula for the mean is:
mean = (3 + 4 + x + 7 + 10)/5
Given that the mean is 6, we can substitute this value into the formula and solve for x:
6 = (3 + 4 + x + 7 + 10)/5
Simplifying the equation:
To simplify the equation, we can start by multiplying both sides of the equation by 5 to eliminate the fraction:
6 * 5 = (3 + 4 + x + 7 + 10)
30 = 3 + 4 + x + 7 + 10
Now, we can combine like terms on the right side of the equation:
30 = 24 + x
Next, we can isolate the variable x by subtracting 24 from both sides of the equation:
30 - 24 = x
6 = x
Conclusion:
Therefore, the value of x is 6. Hence, the correct answer is option D.
If the mean of 3, 4, x, 7, 10 is 6, then the value of x is
Answer:
To find the value of x, we need to use the formula for the mean, which is the sum of all the numbers divided by the total number of numbers.
The formula for the mean is:
mean = (3 + 4 + x + 7 + 10)/5
Given that the mean is 6, we can substitute this value into the formula and solve for x:
6 = (3 + 4 + x + 7 + 10)/5
Simplifying the equation:
To simplify the equation, we can start by multiplying both sides of the equation by 5 to eliminate the fraction:
6 * 5 = (3 + 4 + x + 7 + 10)
30 = 3 + 4 + x + 7 + 10
Now, we can combine like terms on the right side of the equation:
30 = 24 + x
Next, we can isolate the variable x by subtracting 24 from both sides of the equation:
30 - 24 = x
6 = x
Conclusion:
Therefore, the value of x is 6. Hence, the correct answer is option D.
The arithmetic mean of the numerical values of the deviations of items from some average value is called the- a)Standard deviation
- b)Range
- c)Quartile deviation
- d)Mean deviation
Correct answer is option 'D'. Can you explain this answer?
The arithmetic mean of the numerical values of the deviations of items from some average value is called the
a)
Standard deviation
b)
Range
c)
Quartile deviation
d)
Mean deviation
|
|
Maulik Majumdar answered |
Mean deviation of a data set is the average of the absolute deviations from a central point (Average value).
S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is- a)8
- b)6
- c)5
- d)7
Correct answer is option 'B'. Can you explain this answer?
S.D. of a data is 6. When each observation is increased by 1, then the S.D. of new data is
a)
8
b)
6
c)
5
d)
7
|
|
EduRev JEE answered |
Answer: B: 6
Explanation: When a constant is added to every observation in a data set, the spread or dispersion of the data does not change. Therefore, adding 1 to each observation leaves the standard deviation unchanged.
If COV(X,Y) = 0, then the two lines of the regression are- a)parallel
- b)coincident
- c)at right angles
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If COV(X,Y) = 0, then the two lines of the regression are
a)
parallel
b)
coincident
c)
at right angles
d)
none of these
|
|
Learners Habitat answered |
If COV(X,Y)=0, it implies that the covariance between X and Y is zero. This means that there is no linear relationship between the two variables. In such a case, the correlation coefficient ρ(X,Y)=0, and the two lines of regression will be at right angles to each other.
If the two lines of regression are y = 3x – 5 and y = 2x – 4 , then ρ(X,Y) is equal t- a)
- b)
- c)
- d)none of these
Correct answer is option 'C'. Can you explain this answer?
If the two lines of regression are y = 3x – 5 and y = 2x – 4 , then ρ(X,Y) is equal t
a)
b)
c)
d)
none of these
|
|
Tarun Kaushik answered |
To determine the correlation coefficient ρ(X,Y) from the two regression lines, we use the property that the product of the slopes of the two regression lines is equal to ρ 2 .
Given regression lines:
y=3x−5
Slope (m1 ) = 3
Given regression lines:
y=3x−5
Slope (m1 ) = 3
y=2x−4
Slope ( m2) = 2
Step 1: Check the product of slopes
The product of the slopes of the regression lines is:
m 1 ⋅m 2 =3⋅2=6
However, for the two regression lines, the product of their slopes must satisfy:
m1 ⋅m2 =ρ 2
Thus: ρ2 =6
Step 2: Conclusion
Since ρ2 cannot exceed 1, this configuration of regression lines is not possible. Hence, ρ(X,Y) is undefined for the given regression lines.
Slope ( m2) = 2
Step 1: Check the product of slopes
The product of the slopes of the regression lines is:
m 1 ⋅m 2 =3⋅2=6
However, for the two regression lines, the product of their slopes must satisfy:
m1 ⋅m2 =ρ 2
Thus: ρ2 =6
Step 2: Conclusion
Since ρ2 cannot exceed 1, this configuration of regression lines is not possible. Hence, ρ(X,Y) is undefined for the given regression lines.
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Mathematics for EmSAT Achieve
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