## Chapter 7 Statistics R.D. Sharma Solutions for Class 10th Math Exercise 7.6

1. 1. Draw an given by less than method for the following data:
No.of rooms: 1 2 3 4 5 6 7 8 9 10

No. of houses: 4 9 22 28 24 12 8 6 5 2

**Solution**

2. The marks scored by 750 students in an examination are given in the form of a frequency distribution table:

**Solution**

3. Draw an ogive to represent the following frequency distribution:

Class-interval: 0-4 5-9 10-14 15-19 20-24

No. of students: 2 6 10 5 3

**Solution**

4. The monthly profits (in Rs.) of 100 shops are distributed as follows:

Profits per shop: 0-50 50-100 100-150 150-200 200-250 250–300

No. of shops: 12 18 27 20 17 6

Draw the frequency polygon for it.

**Solution**

5. The following distribution the daily income of 50 workers of a factory :

Daily income in : 100-120 120-140 140-160 160-180 180-200

Number of workers : 12 14 8 6 10

Convert the above distribution to a less than type cumulative frequency distribution and draw its ogive .

**Solution**

6. The following table gives production yield per hectare of wheat of 100 farms of a village:

Production yield in kg per hectare: 50-55 55-60 60-65 65-70 70-75 75-80

Number of farms: 2 8 12 24 38 16

Draw ‘less than’ ogive and ‘more than’ ogive.

Draw ‘less than’ ogive and ‘more than’ ogive.

**Solution**

7. During the medical check-up of 35 students of a class, their weights were recorded as follows:

Draw a less than type ogive for the given data. Hence, obtain the median weight from the

graph and verify the result by using the formula .

**Solution**

8. The annual rainfall record of a city for 66 days is given in the following table :

Calculate the median rainfall using ogives of more than type and less than type .

**Solution**

Prepare a table for less than type .

Now, plot the less than ogive using suitable points .

Here, N = 66

N/2 = 33

In order to find the median rainfall , we first locate the point corresponding to 33rd day on the y-axis. Let the point be P. From this point draw a line parallel to the x-axis cutting to curve at Q. From this point Q, draw a line parallel to the y - axis and meeting the x-axis at the point R. The x - coordinate of R is 21.25 .

Thus, median rainfall is is 21.25 cm .

Here , N = 66

N/2 = 33

In order to find the median rainfall, we first locate the point corresponding to 33rd day on the y-axis.Let the point be P.From this point Q, draw a line parallel to the y-axis and meeting the x-axis at the point R. The x-coordinates of R is 21.25.

9. The following table gives the height of tress .

Draw ' less than 'ogive and more than 'ogive'

**Solution**

Consider the following table .

Now draw less than ogive using suitable points .

Now, prepare the cumulative frequency table for men than series .

Now draw more than ogive using suitable points .

10. The annual profits earned by 30 shops of a shopping complex in a locality give rise to the following distribution .

Draw both ogives for the above data and hence obtain the median.

**Solution**

Firstly , we prepare the cumulative frequency table for less than type .

Again, prepare the cumulative frequency table for more than type .

Now, ''more than ogive'' and ''less than ogive'' can be drawn as follows :

The x - coordinate of the point of intersection of the '' more than ogive'' and less- than ogive'' gives the median of the given distribution..

So, the corresponding median is 17.5 lakh .