RD Sharma MCQs: Measures of Central Tendency | Mathematics (Maths) Class 9 PDF Download

 Page 1


Q u e s t i o n : 6 5
Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?
a
Mean
b
Range
c
Median
d
Mode
S o l u t i o n :
We know that mean, median and mode are all measures of central tendency.
Hence, the correct choice is b
.
Q u e s t i o n : 6 6
The mean of n observations is X. If k is added to each observation, then the new mean is
a
X
b
X + k
c
X - k
d
kX
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Add a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Page 2


Q u e s t i o n : 6 5
Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?
a
Mean
b
Range
c
Median
d
Mode
S o l u t i o n :
We know that mean, median and mode are all measures of central tendency.
Hence, the correct choice is b
.
Q u e s t i o n : 6 6
The mean of n observations is X. If k is added to each observation, then the new mean is
a
X
b
X + k
c
X - k
d
kX
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Add a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is b
.
Q u e s t i o n : 6 7
The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is
a
k
¯
X
b
¯
X
k
c
¯
X +k
d
¯
X -k
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Multiply a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is a
.
Q u e s t i o n : 6 8
The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers
is 78. The value of discarded number is
Page 3


Q u e s t i o n : 6 5
Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?
a
Mean
b
Range
c
Median
d
Mode
S o l u t i o n :
We know that mean, median and mode are all measures of central tendency.
Hence, the correct choice is b
.
Q u e s t i o n : 6 6
The mean of n observations is X. If k is added to each observation, then the new mean is
a
X
b
X + k
c
X - k
d
kX
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Add a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is b
.
Q u e s t i o n : 6 7
The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is
a
k
¯
X
b
¯
X
k
c
¯
X +k
d
¯
X -k
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Multiply a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is a
.
Q u e s t i o n : 6 8
The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers
is 78. The value of discarded number is
a
98
b
99
c
100
d
101
 
S o l u t i o n :
Given that the mean of 7 numbers is 81. Let us denote the numbers by .
If be the mean of the n observations , then we have
Hence the sum of 7 numbers is
If one number is discarded then the mean becomes 78 and the total numbers becomes 6.
Let the number discarded is x.
After discarding one number the sum becomes and then the mean is
But it is given that after discarding one number the mean becomes 78.
Hence we have
Thus the excluded number is . So, the correct choice is b
.
Q u e s t i o n : 6 9
For which set of numbers do the mean, median and mode all have the same value?
a
2, 2, 2, 2, 4
b
1, 3, 3, 3, 5
Page 4


Q u e s t i o n : 6 5
Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?
a
Mean
b
Range
c
Median
d
Mode
S o l u t i o n :
We know that mean, median and mode are all measures of central tendency.
Hence, the correct choice is b
.
Q u e s t i o n : 6 6
The mean of n observations is X. If k is added to each observation, then the new mean is
a
X
b
X + k
c
X - k
d
kX
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Add a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is b
.
Q u e s t i o n : 6 7
The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is
a
k
¯
X
b
¯
X
k
c
¯
X +k
d
¯
X -k
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Multiply a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is a
.
Q u e s t i o n : 6 8
The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers
is 78. The value of discarded number is
a
98
b
99
c
100
d
101
 
S o l u t i o n :
Given that the mean of 7 numbers is 81. Let us denote the numbers by .
If be the mean of the n observations , then we have
Hence the sum of 7 numbers is
If one number is discarded then the mean becomes 78 and the total numbers becomes 6.
Let the number discarded is x.
After discarding one number the sum becomes and then the mean is
But it is given that after discarding one number the mean becomes 78.
Hence we have
Thus the excluded number is . So, the correct choice is b
.
Q u e s t i o n : 6 9
For which set of numbers do the mean, median and mode all have the same value?
a
2, 2, 2, 2, 4
b
1, 3, 3, 3, 5
c
1, 1, 2, 5, 6
d
1, 1, 1, 2, 5
S o l u t i o n :
For the data 2, 2, 2, 2, 4 of 5 numbers, we have
Since, 2 occurs maximum number of times,
For the data 1, 3, 3, 3, 5 of 5 numbers, we have
Since, 3 occurs maximum number of times,
Hence, the correct choice is b
.
Note that if it happens that the result is not true for the second data then we must follow the same procedure for the
other data’s.
Q u e s t i o n : 7 0
For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?
a
Mean = Median
b
Mean > Mode
c
Mean > Mode
d
Mode = Median
S o l u t i o n :
Page 5


Q u e s t i o n : 6 5
Mark the correct alternative in each of the following:
Which one of the following is not a measure of central value?
a
Mean
b
Range
c
Median
d
Mode
S o l u t i o n :
We know that mean, median and mode are all measures of central tendency.
Hence, the correct choice is b
.
Q u e s t i o n : 6 6
The mean of n observations is X. If k is added to each observation, then the new mean is
a
X
b
X + k
c
X - k
d
kX
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Add a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is b
.
Q u e s t i o n : 6 7
The mean of n observations is X. If each observation is multiplied by k, the mean of new observations is
a
k
¯
X
b
¯
X
k
c
¯
X +k
d
¯
X -k
S o l u t i o n :
Let us take n observations .
If be the mean of the n observations, then we have
Multiply a constant k to each of the observations. Then the observations becomes 
If be the mean of the new observations, then we have
Hence, the correct choice is a
.
Q u e s t i o n : 6 8
The mean of a set of seven numbers is 81. If one of the numbers is discarded, the mean of the remaining numbers
is 78. The value of discarded number is
a
98
b
99
c
100
d
101
 
S o l u t i o n :
Given that the mean of 7 numbers is 81. Let us denote the numbers by .
If be the mean of the n observations , then we have
Hence the sum of 7 numbers is
If one number is discarded then the mean becomes 78 and the total numbers becomes 6.
Let the number discarded is x.
After discarding one number the sum becomes and then the mean is
But it is given that after discarding one number the mean becomes 78.
Hence we have
Thus the excluded number is . So, the correct choice is b
.
Q u e s t i o n : 6 9
For which set of numbers do the mean, median and mode all have the same value?
a
2, 2, 2, 2, 4
b
1, 3, 3, 3, 5
c
1, 1, 2, 5, 6
d
1, 1, 1, 2, 5
S o l u t i o n :
For the data 2, 2, 2, 2, 4 of 5 numbers, we have
Since, 2 occurs maximum number of times,
For the data 1, 3, 3, 3, 5 of 5 numbers, we have
Since, 3 occurs maximum number of times,
Hence, the correct choice is b
.
Note that if it happens that the result is not true for the second data then we must follow the same procedure for the
other data’s.
Q u e s t i o n : 7 0
For the set of numbers 2, 2, 4, 5 and 12, which of the following statements is true?
a
Mean = Median
b
Mean > Mode
c
Mean > Mode
d
Mode = Median
S o l u t i o n :
For the data 2, 2, 4, 5, 12 of 5 numbers, we have
Since, 2 occurs maximum number of times,
So, the correct choice is b
.
Q u e s t i o n : 7 1
If the arithmetic mean of 7, 5, 13, x and 9 is 10, then the value x is
a
10
b
12
c
14
d
16
S o l u t i o n :
The given data is 7, 5, 13, x and 9. They are 5 in numbers.
The mean is
But, it is given that the mean is 10. Hence, we have
Hence, the correct choice is d
.
Q u e s t i o n : 7 2
If the mean of five observations x, x+2, x+4, x+6, x+8, is 11, then the mean of first three observations is
a