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 |
Solution:
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
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
Now,
Median =
=
=
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:
(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.
