SELINA Solutions for Class 9 Maths Chapter 19 - Mean and Median (For Ungrouped Data Only)

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Chapter 19 - Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(A)

Question 1

Find the mean of 43, 51, 50, 57 and 54.

Solution 1

The numbers given are Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

The mean of the given numbers will be

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 2

Find the mean of first six natural numbers.

Solution 2

The first six natural numbers are Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

The mean of first six natural numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 3

Find the mean of first ten odd natural number.

Solution 3

The first ten odd natural numbers are Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

The mean of first ten odd numbers

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 4

Find the mean of all factors of 10.

Solution 4

The all factors of 10 are Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

The mean of all factors of 10 are

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 5

Find the mean of x + 3, x + 5, x + 7, x + 9 and x + 11.

Solution 5

The given values are Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

The mean of the values are

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 6

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 Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only(ii) the value of Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Solution 6

(i)The given numbers areSelina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

(ii) The value of Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

We know that

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

Here

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Therefore

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data OnlySelina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 7

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%

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

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

(v)resulting mean increased by 60%

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

(vi)resulting mean decreased by 20%

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

 

 

Question 8

The mean of 5 numbers is 18. If one number is excluded, the mean of remaining number becomes 16. Find the excluded number.

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

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Onlytotal of 5 observations-total of 4 observations

= 90 - 64

= 26

Question 9

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.

Solution 9

(i)Given that the mean of observations x, x + 2, x + 4, x + 6 and x + 8 is 11

Mean=Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

(ii)The mean of first three observations are

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 10

The mean of 100 observations is 40. It is found that an observation 53 was misread as 83. Find the correct mean.

Solution 10

Given the mean of 100 observations is 40.

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

 

Incorrect value of x=4000

Correct value of x=Incorrect value of x-Incorrect observation + correct observation

=4000-83+53

=3970

 

Correct mean

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

 

Question 11

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.

Solution 11

Given that the mean of 200 items was 50.

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Incorrect value of Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Correct value of

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Correct mean

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 12

Find the mean of 75 numbers, if the mean of 45 of them is 18 and the mean of the remaining ones is 13.

Solution 12

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 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.

Solution 13

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 14

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.

Solution 14

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 15

Find x if 9, x, 14, 18 x, x, 8, 10 and 4 have a mean of 11.

Solution 15

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 16

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.

Solution 16

Total number of tests = 8

Average score of A = 25

Let the score of 8th test be x.

Then, total score of 8 tests = 29 + 26 + 18 + 20 + 27 + 24 + 29 + x

Now, we have

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Thus, A scored 27 marks in the eights test.

Chapter 19 - Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(B)

Question 1

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.

Solution 1

(i)Firstly arrange the numbers in ascending order

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Now since

n=9(odd)

Therefore Median

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Thus the median is Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only


(ii)

Firstly arrange the numbers in ascending order

241, 243, 257, 258, 261, 271, 292, 299, 327, 347, 350

 

Now since n=11(Odd)

 

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only



(iii) Firstly arrange the numbers in ascending order

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Now since n=10(even)

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Thus the median is Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

 

(iv) Firstly arrange the numbers in ascending order

173,185,189,194,194,200,204,208,220,223

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Thus the median is 197

Question 2

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.

Solution 2

Given numbers are 34, 37, 53, 55, x, x+2, 77, 83, 89, 100

Here n = 10(even)

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only


Question 3

In 10 numbers, arranged in increasing order, the 7th number is increased by 8, how much will the median be changed?

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

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Thus, for n = 10, we have

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Hence, if 7th number is diminished by 8, there is no change in the median value.

Question 4

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.

Solution 4

Here, total observations = n = 10 (even)

Thus, we have

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

According to given information, data in ascending order is as follows:

 

1st

Term

2nd Term

3rd Term

4th Term

5th Term

6th Term

7th Term

8th Term

9th Term

10th Term

Marks

Less than 30

35

40

48

66

More than 75

 

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Hence, the median score of the whole group is 44.

Question 5

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.

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Chapter 19 - Mean and Median (For Ungrouped Data Only) Exercise Ex. 19(C)

Question 1

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%

Solution 1

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

(i) Multiplied by 3

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

(ii) Divided by 2

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

(iii) multiplied by 3 and then divided by 2

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

(iv) increased by 25%

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

(v) decreased by 40%

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 2

The mean of 18, 24, 15, 2x + 1 and 12 is 21. Find the value of x. 

Solution 2

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 3

The mean of 6 numbers is 42. If one number is excluded, the mean of remaining number is 45. Find the excluded number. 

Solution 3

 

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

 

Question 4

The mean of 10 numbers is 24. If one more number is included, the new mean is 25. Find the included number. 

Solution 4

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 5

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.

Solution 5

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 6

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.

Solution 6

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 7

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.

Solution 7

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

(i)

Let us tabulate the observations and their deviations from the mean

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

 

(ii)

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 8

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?

Solution 8

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

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.

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

If 51 is replaced by 66, the new set of data in ascending order is:

35, 48, 52, 63, 64, 66, 71, 76, 92

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 9

The mean of x, x + 2, x + 4, x + 6 and x + 8 is 11, find the mean of the first three observations.

Solution 9

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 10

Find the mean and median of all the positive factors of 72.

Solution 10

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Therefore, the data set is:

1, 2, 3, 4, 6, 8, 9, 12, 18, 24, 36, 72

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only 

Question 11

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.

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

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Hence, the number of boys is 30 and the number of girls is also 30.

Question 12

The average of n numbers x1, x2, x3 ….. xn is A. If x1 is replaced by (x+ α)x1, x2, is replaced by (x+ α)x2 and so on. Find the new average.

Solution 12

Mean of n numbers = A

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

Question 13

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.

Solution 13

Total number of players in each team = 7

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

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)

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only

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)

Selina Solutions Icse Class 9 Mathematics Chapter - Mean And Median For Ungrouped Data Only