NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.2

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

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

NCERT Solutions for Class 9 Maths Chapter 14 Statistics Ex 14.2 are the part of NCERT Solutions for Class 9 Maths. Here you can find the NCERT Solutions for 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 required frequency distribution table is as follows:

From the above table, the most common blood group is O and the 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:
Here, the observation with minimum and maximum values are 2 and 32, respectively.
The class intervals are as follows:
0 – 5, 5 – 10, 10 – 15, 15 – 20, 20 – 25, 25 – 30, 30 – 35
The required frequency distribution table is as follows:

From the above table we observe that:
(i) Frequencies of class intervals 5 – 10 and 10 – 15 are equal, i.e., 11 each. It shows that the maximum number of engineers have their residences at 5 to 15 km away from their work place.
(ii) Frequencies of class intervals 20 – 25 and 25 – 30 are also equal, i.e., 1 each. It shows that the minimum number of engineers have their residences at 20 to 30 km away from their work place.

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:

(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:
Here, the lowest value of observation = 84.9
The highest value of observation = 99.2
So, class intervals are 84 – 86, 86 – 88, 88 – 90, ……., 98 – 100

(i) Thus, the required frequency distribution table is as follows:

(ii) Since, the relative humidity is high during the rainy season, so, the data appears to be taken in the rainy season.
(iii) Range = (Highest observation) – (Lowest observation) = 99.2 – 84.9 = 14.3

Ex 14.2 Class 9 Maths Question 4.
The heights of 50 students, measured to the nearest centimetres have been found to be as follows:

(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 form the table?

Solution:
(i) Here, the lowest value of the observation = 150
The highest value of the observation = 173
So, the class intervals are 150 – 155, 155 -160, …, 170 – 175.
The required frequency distribution table is as follows:

(ii) From the above table, we can conclude that more than 50% of the students are shorter than 165 cm.

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:

(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 day’s was the concentration of sulphur dioxide more than 0.11 parts per million?

Solution:
(i) Here, the lowest value of the observation = 0.01
The highest value of the observation = 0.22
So, the class intervals are 0.00 – 0.04, 0.04 – 0.08, …., 0.20 – 0.24
The required frequency distribution table is as follows:

(ii) The concentration of sulphur dioxide was more than 0.11 ppm for 8 days.

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:
The required frequency distribution table is as follows:

Ex 14.2 Class 9 Maths Question 7.
The value of Ï€ 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:
(i) The required frequency distribution table is as follows:

(ii) The most frequently occurring digits are 3 and 9 and the least frequently occurring digit is 0.

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) Here, the lowest value of the observation = 1 and the highest value of the observation = 17

So, the class intervals are 0 – 5, 5 – 10, 15 – 20
The required frequency distribution table is as follows:

(ii) Number of children who watched television for 15 or more hours in a week is 2.

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:

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

Solution:
Here, the lowest value of the observation = 2.2
and the highest value of the observation = 4.6
So, the class intervals are 2.0 – 2.5, 2.5 – 3.0, …., 4.5 – 5.0
The required frequency distribution table is as follows: