ML Aggarwal Solution Class 9 Chapter 20 Statistics Exercise 20.3

 Exercise 20.3

Question 1

Sol :
The required bar group as shown below

Scale on y-axis=1 unit=30 cm






















Question 2

Sol :
The bar graph required is shown below

Scale on y-axis 1 unit = 50 cm




















Question 3

Sol :
The required bar graph is shown below
Scale on x-axis 1 cm=1 unit
Scale on y-axis 10 cm=1 unit



















Question 4

Sol :
The required horizontal bar graph as shown below
Scale on y-axis 1 unit = 5 cm






















Question 5

Sol :
The required bar graph as shown below
Scale on y-axis 1 unit = 10 cm






















Question 6

Sol :
The histogram is shown below

Scale on x-axis 1 unit=10 cm
Scale on y-axis 1 unit=1 cm





















Question 7

Sol :
The required histogram is shown below
Scale on x-axis 1 unit = 100 cm
Scale on y-axis 1 unit = 5 cm





















Question 8

Sol :
The required histogram as shown below
Scale on x-axis 1 unit = 5 cm
Scale on y-axis 1 unit = 5 cm























Question 9

Sol :
The required histogram as shown below
Scale on x-axis 1 unit = 2 cm
Scale on y-axis 1 unit = 5 cm























Question 10

Sol :
The required histogram as shown below
∴The given frequency distribution is discontinuous , to convert into continuous frequency distribution convert into continuous frequency distribution

Adjustment factor =lower limit of one class - upper limit of previous class / 2
$=\frac{66-65}{2}=\frac{1}{2}$
=0.5

Continuous frequency distribution for the given data is 

Class before adjustment Class after adjustment Frequency
59-65 59.5-65.5 10
66-72 65.5-72.5 5
73-79 72.5-79.5 25
80-86 78.5-86.5 15
87-93 86.5-93.5 30
94-100 93.5-100.5 10

Scale on x-axis 1 unit=6 cm
Scale on y-axis 1 unit=5 cm


















Question 11

Sol :
The required frequency polygon as shown below
Scale on x-axis 1 unit = 10 cm
Scale on y-axis 1 unit = 5 cm




















Question 12

Sol :
The required frequency polygon as shown below
Scale on x-axis 1 unit = 10 cm
Scale on y-axis 1 unit = 5 cm





























Question 13

Sol :
The given frequency distribution is discontinuous, to convert it into a continuous distribution.

Adjustment factor =lower limit of one class - upper limit of previous class / 2

$=\frac{21-20}{2}=\frac{1}{2}$
=0.5

Class before adjustment Class after adjustment Frequency
16-20 16.5-20.5 4
21-25 20.5-25.5 12
26-30 25.5-30.5 18
31-35 30.5-35.5 26
36-40 35.5-40.5 14
41-45 40.5-45.5 10
46-50 45.5-50.5 6

Scale on x-axis 1 unit=4 cm
Scale on y-axis 1 unit=5 cm





















Question 14

Sol :

The required frequency polygon as shown below

Scale on x-axis 1 unit=10 cm
Scale on y-axis 1 unit=5 cm



















Question 15

Sol :
The required histogram and frequency polygon as shown below
Scale on x-axis 1 unit=15 cm
Scale on y-axis 1 unit=5 cm




















Question 16

Sol :

The required histogram and frequency polygon as shown below 

Scale on x-axis 1 unit=10 cm
Scale on y-axis 1 unit=5 cm























Question 17

Sol :
Given water bills of 32 houses in a locality are
30, 48, 52, 78 , 103, 85 ,  37, 94 , 72, 73 ,66, 52 , 92 , 65 ,78 ,81 ,64 ,60 ,75 ,78 , 108 ,63 ,71 ,54 ,59 ,75 ,100 ,103 ,35 ,89 ,95 ,73

Class interval 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110
Frequency 3 1 4 5 9 3 3 3

∴The required histogram and frequency polygon as shown below
Scale on x-axis 1 unit = 10 cm
Scale on y-axis 1 unit = 1 cm

















Question 18

Sol :
Class Interval 40-42 42-44 44-46 46-48 48-50 50-52 52-54
Frequency 2 12 7 6 7 4 2

Scale on x-axis 1 unit = 2 cm
Scale on y-axis 1 unit = 1 cm























Question 19

Sol :
(i) 18
(ii) 475-500
(iii) 34
(iv) 
ClassesFrequencyCumulative Frequency
375-40066
400-1251824
425-4501034
450-4752054
475-500458

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