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All questions of January Week 3 for Class 10 Exam
The mean of 1, 2, 3, 4 …n is given by- a)
- b)n/2
- c)
- d)
Correct answer is option 'D'. Can you explain this answer?
The mean of 1, 2, 3, 4 …n is given by
a)
b)
n/2
c)
d)
|
Krishna Iyer answered |
⇒ We have the sequence, 1,2,3.......n
⇒ This is an AP, with the initial term a=1 and the common difference d=1.
∴ The sum of n terms of an AP is given by,
→ Arithmetic mean of n numbers a1,a2,a3,a4,...an is given by the formula
⇒ This is an AP, with the initial term a=1 and the common difference d=1.
∴ The sum of n terms of an AP is given by,
→ Arithmetic mean of n numbers a1,a2,a3,a4,...an is given by the formula
The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is- a)100
- b)40
- c)10
- d)60
Correct answer is option 'A'. Can you explain this answer?
The mean of 15 numbers is 25. If each number is multiplied by 4, mean of the new numbers is
a)
100
b)
40
c)
10
d)
60
|
Anmol Das answered |
Answer:
100
Step-by-step explanation:
mean=25
every number is multiplied by 4,
then 4 is common
Therefore, 25x4=100
The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. The excluded number is- a)45
- b)36
- c)30
- d)25
Correct answer is option 'B'. Can you explain this answer?
The mean of five numbers is 28. If one of the numbers is excluded, the mean gets reduced by 2. The excluded number is
a)
45
b)
36
c)
30
d)
25
|
Vikas Kumar answered |
Mean of 5 nos.= 28
Therefore, sum of the 5 nos. = 28 * 5 = 140
The the no. exclude by 'x'.
New sum of 4 nos.= 140 - x
New mean = 28- 2 = 26
Therefore, (140 - x ) / 4 = 26
=> 140 - x = 104
=> x = 36
ANSWER= 36
The mean of the following data is: 45, 35, 20, 15, 25, 40- a)15
- b)25
- c)30
- d)35
Correct answer is option 'C'. Can you explain this answer?
The mean of the following data is: 45, 35, 20, 15, 25, 40
a)
15
b)
25
c)
30
d)
35
|
Pankaj verma answered |
Mean of Data Set
To find the mean of a data set, we add up all the numbers in the set and then divide by the total number of values in the set.
Calculation
To find the mean of the given data set, we need to add up all the numbers in the set and then divide by the total number of values in the set:
Mean = (45 + 35 + 20 + 15 + 25 + 40) / 6
Mean = 180 / 6
Mean = 30
Therefore, the mean of the given data set is 30. The correct answer is option C.
To find the mean of a data set, we add up all the numbers in the set and then divide by the total number of values in the set.
Calculation
To find the mean of the given data set, we need to add up all the numbers in the set and then divide by the total number of values in the set:
Mean = (45 + 35 + 20 + 15 + 25 + 40) / 6
Mean = 180 / 6
Mean = 30
Therefore, the mean of the given data set is 30. The correct answer is option C.
The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is- a)28
- b)29
- c)31
- d)30
Correct answer is option 'B'. Can you explain this answer?
The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. Value of this 13th observation is
a)
28
b)
29
c)
31
d)
30
|
Anita Menon answered |
Suppose be all twelevth terms = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
Mean = Terms / Observation
19 . 25 = x / 12
x = 19.25 × 12
x = 231 .00
Now let thirteenth term will be y
Mean = 20
So, 20 = x + y / 13
20 = 231 + y / 13
20 × 13 = 231 + x
260 = 231 + x
260 - 231 = x
29 = x
The mean of first ten even natural numbers is- a)100
- b)11
- c)30
- d)10
Correct answer is option 'B'. Can you explain this answer?
The mean of first ten even natural numbers is
a)
100
b)
11
c)
30
d)
10
|
|
Anmol Das answered |
Mean of First Ten Even Natural Numbers
To find the mean of the first ten even natural numbers, we need to add all the even numbers and divide the sum by the total number of even numbers. The first ten even natural numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
1. Add up the Even Numbers
Add up all the even numbers:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110
2. Divide the Sum by the Total Number of Even Numbers
Since there are 10 even numbers in the list, we divide the sum by 10:
110 ÷ 10 = 11
Therefore, the mean of the first ten even natural numbers is 11. Option 'B' is the correct answer.
To find the mean of the first ten even natural numbers, we need to add all the even numbers and divide the sum by the total number of even numbers. The first ten even natural numbers are:
2, 4, 6, 8, 10, 12, 14, 16, 18, 20
1. Add up the Even Numbers
Add up all the even numbers:
2 + 4 + 6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 = 110
2. Divide the Sum by the Total Number of Even Numbers
Since there are 10 even numbers in the list, we divide the sum by 10:
110 ÷ 10 = 11
Therefore, the mean of the first ten even natural numbers is 11. Option 'B' is the correct answer.
The mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is:- a)6
- b)4
- c)7
- d)11
Correct answer is option 'C'. Can you explain this answer?
The mean of 5 observations x, x + 2, x + 4, x + 6 and x + 8 is 11, then the value of x is:
a)
6
b)
4
c)
7
d)
11
|
|
Krishna Iyer answered |
(x + x + 2 + x + 4 + x + 6 + x + 8) / 5 = 11
5x + 20 = 55
5x = 35 ⇒ x = 7
5x + 20 = 55
5x = 35 ⇒ x = 7
The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is- a)28
- b)29
- c)30
- d)31
Correct answer is option 'B'. Can you explain this answer?
The mean of a data set with 12 observations is calculated as 19.25. If one more value is included in the data, then for the new data with 13 observations, mean becomes 20. The value of this 13th observation is
a)
28
b)
29
c)
30
d)
31
|
Hitesh naidu answered |
Given: Mean of a data set with 12 observations = 19.25
Mean of the new data set with 13 observations = 20
To find: Value of the 13th observation
Step-by-step solution:
1. We know that the formula for calculating the mean of a data set is:
Mean = (Sum of all observations) / (Number of observations)
2. Using this formula, we can write two equations for the given information:
19.25 = (Sum of 12 observations) / 12 ... equation (1)
20 = (Sum of 13 observations) / 13 ... equation (2)
3. From equation (1), we can find the sum of the 12 observations:
Sum of 12 observations = 19.25 x 12 = 231
4. Substituting this value in equation (2), we get:
20 = (231 + 13th observation) / 13
Multiplying both sides by 13, we get:
260 = 231 + 13th observation
Subtracting 231 from both sides, we get:
13th observation = 29
Therefore, the value of the 13th observation is 29.
Mean of the new data set with 13 observations = 20
To find: Value of the 13th observation
Step-by-step solution:
1. We know that the formula for calculating the mean of a data set is:
Mean = (Sum of all observations) / (Number of observations)
2. Using this formula, we can write two equations for the given information:
19.25 = (Sum of 12 observations) / 12 ... equation (1)
20 = (Sum of 13 observations) / 13 ... equation (2)
3. From equation (1), we can find the sum of the 12 observations:
Sum of 12 observations = 19.25 x 12 = 231
4. Substituting this value in equation (2), we get:
20 = (231 + 13th observation) / 13
Multiplying both sides by 13, we get:
260 = 231 + 13th observation
Subtracting 231 from both sides, we get:
13th observation = 29
Therefore, the value of the 13th observation is 29.
) of a frequency distribution is 45. If the value of 
= 20 then the value of 
is:
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