Monday, June 1, 2020

NCERT solution class 10 chapter 14 Statistics exercise 14.4 mathematics

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EXERCISE 14.4


Q 1, Ex 14.4 - Statistics - Chapter 14 - Maths Class 10th - NCERT

Page No 293:

Question 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
Number of workers
12
14
8
6
10
Convert the distribution above to a less than type cumulative frequency distribution, and draw its ogive.

Answer:

The frequency distribution table of less than type is as follows.
Daily income (in Rs)
(upper class limits)
Cumulative frequency
Less than 120
12
Less than 140
12 + 14 = 26
Less than 160
26 + 8 = 34
Less than 180
34 + 6 = 40
Less than 200
40 + 10 = 50
Taking upper class limits of class intervals on x-axis and their respective frequencies on y-axis, its ogive can be drawn as follows.

Q 2, Ex 14.4 - Statistics - Chapter 14 - Maths Class 10th - NCERT


Question 2:

During the medical check-up 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 verify the result by using the formula.

Answer:

The given cumulative frequency distributions of less than type are
Weight (in kg)
upper class limits
Number of students
(cumulative frequency)
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
Taking upper class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be drawn as follows.

Here, n = 35
So,  = 17.5
Mark the point A whose ordinate is 17.5 and its x-coordinate is 46.5. Therefore, median of this data is 46.5.

It can be observed that the difference between two consecutive upper class limits is 2. The class marks with their respective frequencies are obtained as below.
Weight (in kg)
Frequency (f)
Cumulative frequency
Less than 38
0
0
38 − 40
3 − 0 = 3
3
40 − 42
5 − 3 = 2
5
42 − 44
9 − 5 = 4
9
44 − 46
14 − 9 = 5
14
46 − 48
28 − 14 = 14
28
48 − 50
32 − 28 = 4
32
50 − 52
35 − 32 = 3
35
Total (n)
35
The cumulative frequency just greater thanis 28, belonging to class interval 46 − 48.
Median class = 46 − 48
Lower class limit (l) of median class = 46
Frequency (f) of median class = 14
Cumulative frequency (cf) of class preceding median class = 14
Class size (h) = 2

Therefore, median of this data is 46.5.
Hence, the value of median is verified.


Q 3, Ex 14.4 - Statistics - Chapter 14 - Maths Class 10th - NCERT

Question 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
Number of farms
2
8
12
24
38
16
Change the distribution to a more than type distribution and draw ogive.

Answer:

The cumulative frequency distribution of more than type can be obtained as follows.
Production yield
(lower class limits)
Cumulative frequency
more than or equal to 50
100
more than or equal to 55
100 − 2 = 98
more than or equal to 60
98 − 8 = 90
more than or equal to 65
90 − 12 = 78
more than or equal to 70
78 − 24 = 54
more than or equal to 75
54 − 38 = 16
Taking the lower class limits on x-axis and their respective cumulative frequencies on y-axis, its ogive can be obtained as follows.

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