Chapter 19 : Mean and Median (For Ungrouped Data Only)  Selina Solutions for Class 9 Maths ICSE
Mathematics in ICSE Class 9 is one of the most challenging and trickiest subjects of all. It includes complex topics such as logarithms, expansions, indices and Pythagoras Theorem which are difficult to understand for an average student. TopperLearning provides study materials for ICSE Class 9 Mathematics to make the subject easy and help students to clear all their concepts. Our study materials comprise numerous video lessons, question banks, revision notes and sample papers which help achieve success in the examination.
Chapter 19  Mean and Median (For Ungrouped Data Only) Excercise Ex. 19(A)
Find the mean of 43, 51, 50, 57 and 54.
The numbers given are _{}
The mean of the given numbers will be
_{}
Find the mean of first six natural numbers.
The first six natural numbers are _{}
The mean of first six natural numbers
_{}
_{}
Find the mean of first ten odd natural number.
The first ten odd natural numbers are _{}
The mean of first ten odd numbers
_{}
Find the mean of all factors of 10.
The all factors of 10_{ }are _{}
The mean of all factors of 10 are
_{}
Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.
The given values are _{}
The mean of the values are
_{}
If different values of variable x are 9.8, 5.4, 3.7, 1.7, 1.8, 2.6, 2.8, 8.6, 10.5 and 11.1; find
(i) the mean _{}(ii) the value of _{}
(i)The given numbers are_{}
_{}
(ii) The value of _{}
We know that
_{}
Here
_{}
Therefore
_{}
_{}_{}
_{}
The mean of 15 observations is 32. Find the resulting mean, if each observation is :
(i) Increased by 3
(ii) Decreased by 7
(iii) Multiplied by 2
(iv) Divided by 0.5
(v) Increased by 60%
(vi) Decreased by 20%
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%
The mean of 5 numbers is 18. If one number is excluded, the mean of remaining number becomes 16. Find the excluded number.
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
If the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11, find:
(i) The value of x;
(ii) The mean of first three observations.
(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
_{}
The mean of 100 observations is 40. It is found that an observation 53 was misread as 83. Find the correct mean.
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
_{}
The mean of 200 items was 50. Later on, it was discovered that two items were misread as 92 and 8 instead of 192 and 88. Find the correct mean.
Given that the mean of 200 items was 50.
_{}
Incorrect value of _{}
Correct value of
_{}
Correct mean
_{}
Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.
The mean weight of 120 students of a school is 52.75 kg. If the mean weight of 50 of them is 51 kg, find the mean weight of the remaining students.
The mean marks (out of 100) of boys and girls in an examination are 70 and 73 respectively. If the mean marks of all the students in that examination is 71, find the ratio of the number of boys to the number of girls.
Find x if 9, x, 14, 18 x, x, 8, 10 and 4 have a mean of 11.
In a series of tests, A appeared for 8 tests. Each test was marked out of 30 and averages 25. However, while checking his files, A could only find 7 of the 8 tests. For these he scored 29, 26, 18, 20, 27, 24 and 29. Determine how many marks he scored for the eighth test.
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.
Chapter 19  Mean and Median (For Ungrouped Data Only) Excercise Ex. 19(B)
Find the median of:
(i) 25, 16, 26, 16, 32, 31, 19, 28 and 35
(ii) 241, 243, 347, 350, 327, 299, 261, 292, 271, 258 and 257
(iii) 63, 17, 50, 9, 25, 43, 21, 50, 14 and 34
(iv) 233, 173, 189, 208, 194, 204, 194, 185, 200 and 220.
(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
The following data have been arranged in ascending order. If their median is 63, find the value of x.
34, 37, 53, 55, x, x + 2, 77, 83, 89 and 100.
Given numbers are 34, 37, 53, 55, x, x+2, 77, 83, 89, 100
Here n = 10(even)
In 10 numbers, arranged in increasing order, the 7^{th} number is increased by 8, how much will the median be changed?
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 diminished by 8, there is no change in the median value.
Out of 10 students, who appeared in a test, three secured less than 30 marks and 3 secured more than 75 marks. The marks secured by the remaining 4 students are 35, 48, 66 and 40. Find the median score of the whole group.
Here, total observations = n = 10 (even)
Thus, we have
According to given information, data in ascending order is as follows:

1^{st} Term 
2^{nd} Term 
3^{rd} Term 
4^{th} Term 
5^{th} Term 
6^{th} Term 
7^{th} Term 
8^{th} Term 
9^{th} Term 
10^{th} Term 
Marks 
Less than 30 
35 
40 
48 
66 
More than 75 
Hence, the median score of the whole group is 44.
The median of observations 10, 11, 13, 17, x + 5, 20, 22, 24 and 53 (arranged in ascending order) is 18; find the value of x.
Chapter 19  Mean and Median (For Ungrouped Data Only) Excercise Ex. 19(C)
Find the mean of 8, 12, 16, 22, 10 and 4. Find the resulting mean, if each of the observations, given above, be:
(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%
_{}
(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%
_{}
The mean of 18, 24, 15, 2x + 1 and 12 is 21. Find the value of x.
_{}
The mean of 6 numbers is 42. If one number is excluded, the mean of remaining number is 45. Find the excluded number.
_{}
The mean of 10 numbers is 24. If one more number is included, the new mean is 25. Find the included number.
_{}
The following observations have been arranged in ascending order. If the median of the data is 78, find the value of x.
44, 47, 63, 65, x + 13, 87, 93, 99, 110.
_{}
The following observations have been arranged in ascending order. If the median of these observations is 58, find the value of x.
24, 27, 43, 48, x  1, x + 3, 68, 73, 80, 90.
_{}
Find the mean of the following data:
30, 32, 24, 34, 26, 28, 30, 35, 33, 25
(i) Show that the sum of the deviations of all the given observation from the mean is zero.
(ii) Find the median of the given data.
_{}
(i)
Let us tabulate the observations and their deviations from the mean
_{}
(ii)
_{}
Find the mean and median of the data:
35, 48, 92, 76, 64, 52, 51, 63 and 71.
If 51 is replaced by 66, what will be the new median?
_{}
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
_{}
The mean of x, x + 2, x + 4, x + 6 and x + 8 is 11, find the mean of the first three observations.
_{}
Find the mean and median of all the positive factors of 72.
_{}
Therefore, the data set is:
1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72
_{}
The mean weight of 60 students in a class is 40 kg. The mean weight of boys is 50 kg while that of girls is 30 kg. Find the number of boys and girls in the class.
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.
The average of n numbers x_{1}, x_{2}, x_{3} ….. x_{n} is A. If x_{1} is replaced by (x+ α)x_{1}, x_{2}, is replaced by (x+ α)x_{2} and so on. Find the new average.
Mean of n numbers = A
The heights (in cm) of the volley ball players from team A and team B were recorded as:
Team A: 180, 178, 176, 181, 190, 175, 187
Team B: 174, 175, 190, 179, 178, 185, 177
Which team had the greater average height?
Find the median of team A and team B.
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)
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