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**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 : **

👉 Chapter 15 👈