NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.2 are part of NCERT Solutions for Class 9 Maths. Here we have given NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.2.

- Statistics Class 9 Ex 14.1
- Statistics Class 9 Ex 14.2
- Statistics Class 9 Ex 14.3
- Statistics Class 9 Ex 14.4

Board |
CBSE |

Textbook |
NCERT |

Class |
Class 9 |

Subject |
Maths |

Chapter |
Chapter 14 |

Chapter Name |
Statistics |

Exercise |
Ex 14.2 |

Number of Questions Solved |
9 |

Category |
NCERT Solutions |

## NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.2

Ex 14.2 Class 9 Maths Question 1.

**The blood groups of 30 students of class VIII are recorded as follows:
**A, B, O, O, AB, O, A, O, B, A, O, B, A, O, O

A, AB, O, A, A, O, O, AB, B, A, O, B, A, B, O

Represent this data in the form of a frequency distribution table. Which is the most common and which is the rarest, blood group among these students?

Solution.

The number of students who have a certain type of blood group is called the frequency of those blood groups. To make data more easily understandable, we write it in a table, as given below :

Blood Group |
Number of students |

A | 9 |

B | 6 |

0 | 12 |

AB | 3 |

Total |
30 |

From table, we observe that the higher frequency blood group i.e., most common blood group is O and the lowest frequency blood group i.e., rarest blood group is AB.

Ex 14.2 Class 9 Maths Question 2.

The distance (in km) of 40 engineers from their residence to their place of work were found as follows :

5 | 3 | 10 | 20 | 25 | 11 | 13 | 7 | 12 | 31 |

19 | 10 | 12 | 17 | 18 | 11 | 32 | 17 | 16 | 2 |

7 | 9 | 7 | 8 | 3 | 5 | 12 | 15 | 18 | 3 |

12 | 14 | 2 | 9 | 6 | 15 | 15 | 7 | 6 | 12 |

Construct a grouped frequency distribution table with class size 5 for the data given above taking the first interval as 0-5 (5 not included). What main features do you observe from this tabular representation?

Solution.

To present such a large amount of data, so that a reader can make sense of jt easily, we condense it into groups like 0-5, 5-10,…, 30-35 (since, our data is from 5 to 32). These grouping are called ‘classes’ or ‘class-intervals’ and their size is called the class size or class width which is 5 in this case. In each of these classes the least number is called the lower class limit and the greatest number is called the upper class limit e.g., in 0-5, 0 is the ‘lower class limit’ and 5 is the ‘upper class limit’. Now, using tally marks, the data (given) can be condensed in tabular form as follows :

Presenting data in this form simplifies and condenses data and enables us to observe certain important feature at a glance. This is called a grouped frequency distribution table. We observe that the classes in the table above are non-overlapping.

Ex 14.2 Class 9 Maths Question 3.

The relative humidity (in %) of a certain city for a month of 30 days was as follows :

98.1 | 98.6 | 99.2 | 90.3 | 86.5 | 95.3 | 92.9 | 96.3 | 94.2 | 95.1 |

89.2 | 92.3 | 97.1 | 93.5 | 92.7 | 95.1 | 97.2 | 93.3 | 95.2 | 97.3 |

96.2 | 92.1 | 84.9 | 90.2 | 95.7 | 98.3 | 97.3 | 96.1 | 92.1 | 89.0 |

**(i)** Construct a grouped frequency distribution table with classes 84-86, 86-88 etc.

**(ii)** Which month or season do you think this data is about?

**(iii)** What is the range of this data?

Solution.

**(i)** We condense the given data into groups, like 84-86, 86-88, …98-100 (since, our data is from 84.9 to 99.2). So, the class width in this case is 2. Now, the given data can be condensed in tabular form as follows :

**(ii)** From the table, we observe that the data appears to be taken in the rainy season as the relative humidity is high.

**(iii)** We know that,

Range = Upper limit of data – Lower limit of data = 99.2 – 84.9 = 14.3

Ex 14.2 Class 9 Maths Question 4.

The heights of 50 students, measured to the nearest centimeters have been found to be as follows :

161 | 150 | 154 | 165 | 168 | 161 | 154 | 162 | 150 | 151 |

162 | 164 | 171 | 165 | 158 | 154 | 156 | 172 | 160 | 170 |

153 | 159 | 161 | 170 | 162 | 165 | 166 | 168 | 165 | 164 |

154 | 152 | 153 | 156 | 158 | 162 | 160 | 161 | 173 | 166 |

161 | 159 | 162 | 167 | 168 | 159 | 158 | 153 | 154 | 159 |

**(i)** Represent the data given above by a grouped frequency distribution table, taking class intervals as 160-165, 165-170 etc.

(ii) What can you conclude about their heights from the table?

Solution.

**(i)** We condense the given data into groups like 150-155, 155-160…170-175 (since, our data is from 150 to 172). The class width in this case is 5.

** Now, the given data can be condensed in tabular form as follows :
**

**(ii)** From the table, our conclusion is that more than 50% of student (i.e., 12 + 9+14 = 3 5) are shorter than 165 cm height.

Ex 14.2 Class 9 Maths Question 5.

A study was conducted to find out the concentration of sulphur dioxide in the air in parts per million (ppm) of a certain city.

**The data obtained for 30 days is as follows :
**

0.03 | 0.08 | 0.08 | 0.09 | 0.04 | 0.17 |

0.16 | 0.05 | 0.02 | 0.06 | 0.18 | 0.20 |

0.11 | 0.08 | 0.12 | 0.13 | 0.22 | 0.07 |

0.08 | 0.01 | 0.10 | 0.06 | 0.09 | 0.18 |

0.11 | 0.07 | 0.05 | 0.07 | 0.01 | 0.04 |

** (i) **Make a grouped frequency distribution table for this data with class intervals as 0.00-0.04, 0.04-0.08 and so on.

**(ii)** For how many days, was the concentration of sulphur dioxide more than 0.11 parts per million (ppm)?

Solution.

**(i)** We condense the given data into groups like 0.00-0.04, 0.04-0.08,…,0.20-0.24. (since, our data is from 0.01 to 0.22). The class width in this case is 0.04.

**Now, the given data can be condensed in tabular form as follows :
**

Concentration of sulphur dioxide (in ppm) |
Frequency |

0.00 – 0.04 | 4 |

0.04 – 0.08 | 9 |

0.08 – 0.12 | 9 |

0.12- 0.16 | 2 |

0.16 – 0.20 | 4 |

0.20 – 0.24 | 2 |

Total |
30 |

**(ii)** The concentration of sulphur dioxide was more than 0.11 ppm for 2 + 4 + 2 = 8 days (by table.)

Ex 14.2 Class 9 Maths Question 6.

Three coins were tossed 30 times simultaneously. Each time the number of heads occurring was noted down as follows :

0 | 1 | 2 | 2 | 1 | 2 | 3 | 1 | 3 | 0 |

1 | 3 | 1 | 1 | 2 | 2 | 0 | 1 | 2 | 1 |

3 | 0 | 0 | 1 | 1 | 2 | 3 | 2 | 2 | 0 |

** **Prepare a frequency distribution table for the data given above.

Solution.

**Firstly, we write the data in a table :**

Number of heads |
Frequency |

0 | 6 |

1 | 10 |

2 | 9 |

3 | 5 |

Total |
30 |

In above table, we observe that the repetition of ‘0’ in given data is 6 times, 1 as to 10 times, 2 as 9 times and 3 as 5 times. Also, the above table is called an ungrouped frequency distribution table or simply a frequency distribution table.

Ex 14.2 Class 9 Maths Question 7.

The value of π upto 50 decimal places is given below: 3.14159265358979323846264338327950288419716939937510

**(i)** Make a frequency distribution of the digits from 0 to 9 after the decimal point.

**(ii)** What are the most and the least frequently occurring digits?

Solution.

**Firstly, we write the data i.e., digits from 0 to 9 after the decimal point in a table below :**

Digits |
Frequency |

0 | 2 |

1 | 5 |

2 | 5 |

3 | 8 |

4 | 4 |

5 | 5 |

6 | 4 |

7 | 4 |

8 | 5 |

9 | 8 |

Total |
50 |

**(i)** From the table, we observe that the digit’s after the decimal points i.e., 0, 1, 2, 3, 4, 5, 6, 7, 8, 9 repeated 2, 5, 5, 8, 4, 5, 4, 4, 5, 8 times, respectively.

**(ii)** From the table, we observe that the digits after the decimal point 3 and 9 are most frequently occurring i.e., 8 times. The digit ‘0’ is the least occurring i.e., only 2 times.

Ex 14.2 Class 9 Maths Question 8.

Thirty children were asked about the number of hours they watched TV programmes in the previous week. The results were found as follows:

1 | 6 | 2 | 3 | 5 | 12 | 5 | 8 | 4 | 8 |

10 | 3 | 4 | 12 | 2 | 8 | 15 | 1 | 17 | 6 |

3 | 2 | 8 | 5 | 9 | 6 | 8 | 7 | 14 | 12 |

**(i)** Make a grouped frequency distribution table for this data, taking class width 5 and one of the class intervals as 5 – 10.

**(ii)** How many children watched television for 15 or more hours a week?

Solution.

**(i)** We condense the given data into groups like 0 – 5, 5 – 10,…, 15 – 20 (since, our data is from 1 to 17). The class width in this case is 5.

**Now, required grouped frequency distribution table is as follows :
**

Number of hours |
Frequency |

0 – 5 | 10 |

5 – 10 | 13 |

10 – 15 | 5 |

15 – 20 | 2 |

Total |
30 |

**(ii)** From the table, we observe that the number of children is 2, who watched television for 15 or more hours a week.

Ex 14.2 Class 9 Maths Question 9.

A company manufactures car batteries of a particular type. The lives (in years) of 40 such batteries were recorded as follows :

2.6 | 3.0 | 3.7 | 3.2 | 2.2 | 4.1 | 3.5 | 4.5 |

3.5 | 2.3 | 3.2 | 3.4 | 3.8 | 3.2 | 4.6 | 3.7 |

2.5 | 4.4 | 3.4 , | 3.3 | 2.9 | 3.0 | 4.3 | 2.8 |

3.5 | 3.2 | 3.9 | 3.2 | 3.2 | 3.1 | 3.7 | 3.4 |

4.6 | 3.8 | 3.2 | 2.6 | 3.5 | 4.2 | 2.9 | 3.6 |

Construct a grouped frequency distribution table for this data, using class intervals of size 0.5 starting from the interval 2 – 2.5.

Solution.

We condense the given data into groups like 2.0 – 2.5, 2.5 – 3.0,…4.5 – 5.0 (Since, our data is from

2.2 to 4.6). The class width in this case is 0.5.

**Now, the given data can be condensed in tabular form as follows :
**

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