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# 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 observations-total 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 x-Incorrect observation + correct observation

=4000-83+53

=3970

Correct mean

### Solution 11

Given that the mean of 200 items was 50.

Incorrect value of

Correct value of

Correct mean

### 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

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 7th 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.

## 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 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 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)