# OP Malhotra Class 9 ICSE Maths Solutions Chapter 14

## OP Malhotra Class 9 ICSE Maths Solutions Chapter 14 Introduction Data and Frequency Distributions

Welcome to NCTB Solutions. Here with this post we are going to help 9th class students for the Solutions of OP Malhotra Class 9 ICSE Math Book, Chapter 14, Introduction Data and Frequency Distributions. Here students can easily find step by step solutions of all the problems for Introduction Data and Frequency Distributions, Exercise 14. Also here our mathematics teacher’s are solved all the problems with easily understandable methods with proper guidance so that all the students can understand easily. Here in this post students will get chapter 14 solutions. Here in this post all the solutions are based on ICSE latest Syllabus.

Introduction Data and Frequency Distributions Exercise 14 Solution :

Question no – (1)

Solution :

(i) The difference between the maximum and the minimum observations in a set of data is called the Range of the data.

(ii) The number of observations in a particular class interval is called the Frequency of the class interval.

Question no – (2)

Solution :

(i) Lower limit of the class interval 26 – 33 is 26

(ii) Upper limit of the class interval 21 – 25 is 25.

(iii) The class mark of the class interval 20-29 is 24.5

Explanation :

= 24.5 (20 + 29/2)

= 24.5

(iv) The class mark of the class interval 9.5-19.5 is 14.5

Explanation :

Class mark,

= 9.5 + 19.5/2

= 29/2

= 14.5

(v) If the class-marks of a distribution are 32, 39, 46, 53; then the width of each class interval is 7

Interval,

(39 – 32) = 7

(46 – 39) = 7

(53 – 46) = 7

(vi) The mid-point of a class interval is called its Class mark.

(vii) If the class marks of a distribution are 28, 34, 40, 46, 52; then the class intervals are of length 6.

Explanation :

= (34 – 28)

= 6

(viii) If the class marks in a frequency distribution are 19.5, 26.5, 33.5, 40.5, 47.5, 54.5, 61.5, then the class size of the distribution is 7.

Question no – (3)

Solution :

(i) The range of the set of data 5, 8, 15, 21, 7, 10 is 5.

(ii) The range of the set of data 15, 13, 14, 17, 19, 16, 14, 15 is 5.

(iii) The class mark of the class interval 10 – 19 is 14.5

Explanation :

= 19 + 10/2

= 29/2

= 14.5

(iv) The class mark of the class interval 9.5 – 16.5 is 13

Explanation :

= 9.5 + 16.5/2

= 26/2

= 13

Question no – (4)

Solution :

(i) Size of shoes,

= Discrete

(ii) Number of pages in a book,

= Continuous

(iii) Distance travelled by a train,

= Continuous

(iv) Time,

= Continuous

(v) Daily temperature,

= Continuous

(vi) intelligence quotient,

= Continuous

(vii) Number of goals scored in a hockey-match,

= Discrete

(viii) Height,

= Continuous

(ix) Weight,

= Continuous

(x) Number of rooms in apartments,

= Discrete

(xi) Number of wage earners in a factory,

= Discrete

(xii) Number of car accidents.

= Discrete

Question no – (5)

Solution :

Here, the class size

= (2.23 – 2.03)

= 0.20

Class boundaries will be,

2.03 – 0.20/2

= 2.03 – 0.10

= 1.93

and, 2.03 + 0.20/2

= 2.03 + 0.10

= 2.13

1 – 93 – 2.13, 2.13 – 2.33, 2.33 – 2.53, 2.53 – 2.73, 2.73 – 2.93, 2.93 – 3.13

Question no – (6)

Solution :

From the data,

Highest rent = 84, lowest rent = 31

∴ Range = 84 – 31

= 53

Class interval 40 – 50 (excluding. 50)

 Interval Tally mark Frequency 30 – 40 |||| | 6 40 – 50 |||| ||| 8 50 – 60 ||| 3 60 – 70 |||| 4 70 – 80 |||| | 6 80 – 90 ||| 3 Total = 30

Question no – (7)

Solution :

Here, Height weight = 8.5

lowest weight = 30

Range = (85 – 30)

= 55

Required Frequency distribution table :

 Interval Tally marks Frequency 30 – 40 ||| 3 40 – 50 |||| | 6 50 – 60 ||| 3 60 – 70 |||| | 5 70 – 80 |||| 5 20 – 90 |||| || 7

Total = 30

Question no – (8)

Solution :

Here, Range

= (192 – 120)

= 72

Now,

 Class Interval Tally marks Frequency 120 – 130 |||| 4 130 – 140 |||| 4 140 – 150 |||| | 5 150 – 160 |||| 6 160 – 170 |||| 4 170 – 180 |||| 4 180 – 190 | 1 190 – 200 || 2

Total = 30

Question no – (9)

Solution :

Here, Range = (93 – 3)

= 90

So now,

 Class Interval Tally marks Frequency 0 – 9 IIII 10 – 19 III 20 – 29 II 30 – 39 IIII III I 40 – 49 IIII II 50 – 59 IIII IIII 60 – 69 IIII IIII I 70 – 79 IIII 80 – 89 IIII 90 – 99 III

Total = 60

Question no – (10)

Solution :

Here, Range

= 79 – 51

= 28

Class in teals

= 51 – 55,

= 56 – 60

Required table :

 Pulse rate Tally marks No of Books 50 – 55 |||| 5 56 – 60 |||| | 6 61 – 65 ||| 3 66 – 75 |||| || 7 71 – 75 |||| || 7 76 – 80 || 2

Total = 30

Next Chapter Solution :

Updated: June 20, 2023 — 8:06 am