# Class 10 RD Sharma Solutions – Chapter 7 Statistics – Exercise 7.5 | Set 2

### Question 11. Find the mean, median, and mode of the following data:

Solution:

Let mean (A) = 175

Find Median:

Here N = 25, 5/3 = 25/2 = 12.5 or 13, it lies in the class interval = 50-200.

l = 150, F = 10, f = 6, h = 50

Using median formula, we get = 150 + 20.83

= 170.83

Find Mean:

Using mean formula we get = 175 – 6

= 169

Find Mode:

Using mode formula we get = 150 + 25

= 175

### Question 12. A student noted the number of cars passing through a spot on a road for 100 periods each of 3 minutes and summarized it in the table given below. Find the mode of the data.

Solution:

From the given table we conclude that

Modal class = 40-50 (it has maximum frequency)

Also,

l = 40, f = 20, f1 = 12, f2 = 11 and h = 10

By using mode formula, we get = 40 + 4.70

= 44.7

### Question 13. The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality. Find the median, mean, and mode of the data and compare them:

Solution:

Let mean (A) = 135

Find Median:

Here, N = 34

N/2 = 34,

Class interval = 25-145

Also,

l = 125, F = 22, f = 20 and h = 20

By using the median formula, we get = 125 + 12

= 137 units

Find Mean:

By using the mean formula, we get

Mean = = 135 + 2.05

= 137.05 units

Find Mode:

By using the mode formula, we get = 125 + 10.76

= 135.76 units

### Determine the median number of letters in the surnames. Find the mean number of letters in the surnames. Also, And the modal size of the surnames.

Solution:

Let mean (A) = 8.5

Find Median:

Here, N = 100

So, N/2 = 50

Class interval = 7-10

l = 7, F = 36, f = 40 and h =3

By using the median formula, we get = 7 + 1.05

= 8.05

Find Mean:

By using the mean formula, we get

Mean = = 8.5 + 0.18

= 8.32

Find Mode:

We have,

N = 100

N/2 = 100/2 = 50

Here, the cumulative frequency is just greater than N/2 = 76,

Hence, the median class = 7 – 10

l = 7, h = 10 – 7 = 3, f = 40, F = 36

By using the mode formula, we get

Mode = l + = 7 + = 7 + 30/34

= 7 + 0.88

= 7.88

### Question 15. Find the mean, median, and mode of the following data:

Solution:

Find Mean:

By using the mean formula, we get

Mean = Find Median:

We have,

N = 50

Then, N/2 = 50/2 = 25

Here, the cumulative frequency just greater than N/2 = 36

Hence, the median class = 60 – 80

l = 60, h = 80 – 60 = 20, f = 12, F = 24

By using the median formula, we get

Median = l + = 60 + = 60 + 20/12

= 60 + 1.67

= 61.67

Find Mode:

We have,

The maximum frequency = 12

Model class = 60 – 80

l = 60, h = 80 – 60 = 20, f = 12, f1 = 10, f2 = 6

By using the mode formula, we get

Mode = l + = 60 + = 60 + 40/8

= 65

### Question 16. The following data gives the distribution of total monthly household expenditure of 200 families of a village. Find the modal monthly expenditure of the families. Also, find the mean monthly expenditure:

Solution:

From the given table we conclude that

The maximum class frequency = 40

So, modal class = 1500 – 2000

l = 1500, f = 40, h = 500, f1 = 24, f2 = 33

By using the mode formula, we get

Mode = l + = 1500 + = 1500 + = 1500 + 347.826

= 1847.826 ≈ 1847.83

Hence, the modal monthly expenditure = Rs. 1847.83

Now we will find class marks as

Class mark = Class size (h) of given data = 500

Let mean(a) = 2750, now we are going to calculate diui as follows:

From the table we conclude that

∑fi = 200

∑fidi = -35

Mean = a + = 2750 + = 2750 – 87.5

= 2662.5

Hence, the mean monthly expenditure = Rs. 2662.5

### Find the mode of the data

Solution:

From the given table we conclude that

The maximum class frequency = 18

So, modal class = 4000 – 5000

and

l = 4000, f = 18, h = 1000, f1 = 4, f2 = 9

By using the mode formula, we get

Mode = l + = 4000 + = 4000 + (14000/23)

= 4000 + 608.695

= 4608.695

Hence, the mode of given data = 4608.7 runs.

### Find the modal agriculture holdings of the village.

Solution:

From the given table we conclude that

The maximum class frequency = 80,

So, the modal class = 5-7

and

l = 5, f0 = 45, h = 2, f1 = 80, f2 = 55

By using the mode formula, we get

Mode = l + = 5 + = 5 + = 5 + = 5 + 1.2

= 6.2

So, the modal agricultural holdings of the village = 6.2 hectares.

### Calculate the modal income.

Solution:

From the given table we conclude that

The maximum class frequency = 41,

So, modal class = 10000-15000.

Here, l = 10000, f1 = 41, f0 = 26, f2 = 16 and h = 5000

Therefore, by using the mode formula, we get

Mode = l + = 10000 + = 10000 + = 10000 + = 10000 + 15 × 125

= 10000 + 1875

= 11875

So, the modal income = Rs. 11875.

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