Class 9 SELINA Solutions Maths Chapter 19  Mean and Median (For Ungrouped Data Only)
Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(A)
Solution 1
The numbers given are _{}
The mean of the given numbers will be
_{}
Solution 2
The first six natural numbers are _{}
The mean of first six natural numbers
_{}
_{}
Solution 3
The first ten odd natural numbers are _{}
The mean of first ten odd numbers
_{}
Solution 4
The all factors of 10_{ }are _{}
The mean of all factors of 10 are
_{}
Solution 5
The given values are _{}
The mean of the values are
_{}
Solution 6
(i)The given numbers are_{}
_{}
(ii) The value of _{}
We know that
_{}
Here
_{}
Therefore
_{}
_{}_{}
_{}
Solution 7
Given that the mean of 15 observations is 32
(i)resulting mean increased by 3
=32 + 3
=35
(ii)resulting mean decreased by 7
_{=32  7}
_{= 25}
(iii)resulting mean multiplied by 2
=32*2
=64
(iv)resulting mean divide by 0.5
_{}
(v)resulting mean increased by 60%
(vi)resulting mean decreased by 20%
Solution 8
Given the mean of 5 numbers is 18
Total sum of 5 numbers
=18*5
=90
On excluding an observation, the mean of remaining 4 observation is 16_{}
_{=16*4}
_{=64}
Therefore sum of remaining 4 observations
_{}total of 5 observationstotal of 4 observations
= 90  64
= 26
Solution 9
(i)Given that the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11
Mean=_{}
_{}
(ii)The mean of first three observations are
_{}
Solution 10
Given the mean of 100 observations is 40.
_{}
Incorrect value of x=4000
Correct value of x=Incorrect value of xIncorrect observation + correct observation
=400083+53
=3970
Correct mean
_{}
Solution 11
Given that the mean of 200 items was 50.
_{}
Incorrect value of _{}
Correct value of
_{}
Correct mean
_{}
Solution 12
Solution 13
Solution 14
Solution 15
Solution 16
Total number of tests = 8
Average score of A = 25
Let the score of 8^{th} test be x.
Then, total score of 8 tests = 29 + 26 + 18 + 20 + 27 + 24 + 29 + x
Now, we have
Thus, A scored 27 marks in the eights test.
Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(B)
Solution 1
(i)Firstly arrange the numbers in ascending order
_{}
Now since
n=9(odd)
Therefore Median
_{}
Thus the median is _{}
(ii)
Firstly arrange the numbers in ascending order
241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350
Now since n=11(Odd)
(iii) Firstly arrange the numbers in ascending order
_{}
Now since n=10(even)
_{}
_{}
Thus the median is _{}
(iv) Firstly arrange the numbers in ascending order
173,185,189,194,194,200,204,208,220,223
_{}
Thus the median is 197
Solution 2
Given numbers are 34, 37, 53, 55, x, x+2, 77, 83, 89, 100
Here n = 10(even)
Solution 3
For any given set of data, the median is the value of its middle term.
Here, total observations = n = 10 (even)
If n is even, we have
Thus, for n = 10, we have
Hence, if 7^{th} number is increased by 8, there is no change in the median value.
Solution 4
Here, total observations = n = 10 (even)
Thus, we have
According to given information, data in ascending order is as follows:

1 
2 
3 
4 
5 
6 
7 
8 
9 
10 
Marks 
Less than 30 
35 
40 
48 
66 
More than 75 
Hence, the median score of the whole group is 44.
Solution 5
Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(C)
Solution 1
_{}
(i) Multiplied by 3
_{}
(ii) Divided by 2
_{}
(iii) multiplied by 3 and then divided by 2
_{}
(iv) increased by 25%
_{}
(v) decreased by 40%
_{}
Solution 2
_{}
Solution 3
_{}
Solution 4
_{}
Solution 5
_{}
Solution 6
_{}
Solution 7
_{}
(i)
Let us tabulate the observations and their deviations from the mean
_{}
(ii)
_{}
Solution 8
_{}
Let us rewrite the given data in ascending order:
Thus, we have
35, 48, 51, 52, 63, 64, 71, 76, 92
There are 9 observations, which is odd.
_{}
If 51 is replaced by 66, the new set of data in ascending order is:
35, 48, 52, 63, 64, 66, 71, 76, 92
_{}
Solution 9
_{}
Solution 10
_{}
Therefore, the data set is:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
_{}
Solution 11
Total number of students = 60
Mean weight of 60 students = 40
Let the number of boys = x
Then, number of girls = 60  x
Hence, the number of boys is 30 and the number of girls is also 30.
Solution 12
Mean of n numbers = A
Solution 13
Total number of players in each team = 7
Thus, team A has greater average height.
Median of team A:
Arranging heights in ascending order, we get
175, 176, 178, 180, 181, 187, 190
Total number of observations = n = 7 (odd)
Median of team B:
Arranging heights in ascending order, we get
174, 175, 177, 178, 179, 185, 190
Total number of observations = n = 7 (odd)