ML Aggarwal Solution Class 9 Chapter 20 Statistics Exercise 20.2

  Exercise 20.2

Question 1

Sol :

(i) discrete 

(ii) continuous 

(iii) discrete 

(iv) continuous 

(v) continuous 


Question 2

Sol :
Given data 
13, 6, 10 ,5 ,11 ,14 ,2 ,8 ,15 ,16 ,9 ,13 ,17 ,11, 19 ,5 ,7 ,12 ,20 ,21 ,18 ,1 ,8 ,12 ,18
Classes 0-4 5-9 10-14 15-9 20-24
Frequency 2 7 8 6 2

Question 3

Sol :
(i) 
Classes 1-10 11-20 21-30
 31-40
Frequency 8 7 6 6

(ii) Range = Maximum value - Minimum value 
=40-2=38

(iii) Third class of frequency table
$=\frac{21+30}{2}=\frac{51}{2}$
=25.5

Question 4

Sol :

Variate : A particular value of a variable is called variate

Class size : The difference between the actual upper limit and the actual lower limit of a class is called its class size.

Class mark : The class mark of a class is the value mid way between its actual limit and actual upper limit.

Class limits : In the discrete distribution , the original class limits are called stated class limits 

True class limit : In a continuous distribution, the class limits are called true class limit (or) actual class limits 

Frequency of a class : The number of times a variate occurs in a given data is called frequency of that variate.

Cumulative frequency of a class : The sum of frequency of all the previous classes and that particular class is called the cumulative frequency of the class 


Question 5

Sol :

(i) frequency

(ii) size 

(iii) 14

(iv) class mark

(v) 6.5


Question 6

Sol :

(i)

Classes 1-10 11-20 21-30 31-40 41-50
Frequency 7 8 7 10 8

(ii)

Classes 0.5-10.5 10.5-20.5 20.5-30.5 30.5-40.5 40.5-50.5
Frequency 7 8 7 10 8

(iii) Lower limit = 20.5

Upper limit = 30.5


(iv) 

$\frac{30 \cdot 5+40 \cdot 5}{2}=\frac{11}{2}$=35.5


Question 7

Sol :

(i) upper limit =52 , lower limit = 48

(ii) upper limit = 52.5 , lower limit =47.5

(iii) 37.5 and 42.5

(iv) 45

(v) 5


Question 8

Sol :

Marks 10-19 20-29 30-39 40-49 50-59 60-69 70-79 80-89
Frequency 7 11 20 46 57 37 15 7
C.frequency 7 18 38 84 141 178 193 200


Question 9

Sol :

Classes  0-10 10-20 20-30 30-40 40-50
Frequency 5 5 7 10 8
C.frequency 5 10 17 27 35

Number of students obtaining below 20 marks =10


Question 10

Sol :

(i)

Classes Tally Marks Frequency Cumulative frequency
0-10 ||| 3 3
10-20 || 2 5
20-30 $\require{cancel}\cancel{||||}~\cancel{||||}~|$ 11 16
30-40 $\require{cancel}\cancel{||||}~\cancel{||||}~\cancel{||||}~|||$ 18 34
40-50 _ _ 34
50-60 ||| 3 37
60-70 || 2 39
70-80 ||| 3 42
80-90 $\require{cancel}\cancel{||||}$ 5 47
90-100 ||| 3 50

(ii) 

The class that has highest frequency is 30-40

(iii)

The students score less than 40 marks are 64

(iv)

13


Question 11

Sol :

Classes 0-4 4-7 7-10 10-13 13-16
Frequency 7 31 137 73 52

Number of children in the age group of 10

10-13=73


Question 12

Sol :
Classes 0-10 11-20 21-30 31-40 41-50 51-60
Frequency 2 5 11 14 11 7

Question 13

Sol :

Class 30-40 40-50 50-60 60-70 70-80 80-90 90-100 100-110
Frequency 2 1 4 4 9 5 3 4


Question 14

Sol :

Class 23.5-27.5 27.5-31.5 31.5-35.5 35.5-39.5 39.5-43.5
Frequency 4 7 4 4 11


Question 15

Sol :

(i) Class size=134-124=10

Lower limit=119 , Upper limit =129


(ii) Class size=30.5-23.5=7

Lower limit = 20 , Upper limit = 27

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