NCERT Solutions Maths Class 10 Exercise 14.4

# NCERT Solutions Maths Class 10 Exercise 14.4

## Maths Class 10 Exercise 14.4

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

 Daily income (in Rs.) 100 – 120 120 – 140 140 – 160 160 – 180 180 – 200 No. of workers 12 14 8 6 10

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

Solution:

Now, by drawing the points on the graph, i.e., (120, 12); (140, 26); (160, 34); (180, 40); (200, 50)

Scale: On x-axis 10 units = Rs. 10 and on y-axis 10 units = 5 workers

2. During the medical checkup of 35 students of a class, their weights were recorded as follows:

 Weight (in kg) Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 35

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:

Hence, the points for graph are:

(38, 0); (40, 3); (42, 5); (44, 9); (46, 14); (48, 28); (50, 32); (52, 35)

Scale: On x-axis, 10 units = 2 kg and on y-axis, 10 units = 5 students

From the above graph, Median = 46.5 kg, which lies in class interval 46 – 48.

Here, Σfi = n = 35, therefore n/2 = 35/2 = 17.5, which lies in interval 46 – 48.

Therefore, the median class = 46 – 48

So, l = 46, n = 35, f = 14, cf = 14 and h = 2

= 46 + 7/14

= 46 + 0.5

= 46.5

Hence, median weight of the students is 46.5 kg.

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

 Production yield (in kg/ha) 50 – 55 55 – 60 60 – 65 65 – 70 70 – 75 75 – 80 No. of farms 2 8 12 24 38 16

Change the distribution to a more than type distribution and draw its ogive.

Solution:

The points for the graph are:

(50, 100); (55, 98); (60, 90); (65, 78); (70, 54); (75, 16)

Scale: On x-axis, 10 units = 5 kg/ha and on y-axis, 10 units = 10 farms.