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NCERT Solutions Class 9 Maths Chapter 14 Statistics Ex 14.2

NCERT Solutions Class 9 Maths
Chapter – 14 (Statistics)

The NCERT Solutions in English Language for Class 9 Mathematics Chapter – 14 Statistics Exercise 14.2 has been provided here to help the students in solving the questions from this exercise. 

Chapter 14: Statistics

Exercise – 14.2

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?

Answer – ‘Frequency’ of a particular data refers to the number of times the data value occurs. In our case, frequency refers to the number of students having the same blood group.
The blood group of 30 students of Class VIII can be shown as follows:

Blood Group Number of Students
(Frequency)
A 9
B 6
O 12
AB 3
Total 30

The most common (most frequently occurring) blood group is ‘O’.
The rarest blood group (least frequently occurring) is ‘AB.’

2. The distance (in km) of 40 engineers from their residence to their place of work was 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?

Answer – Since the given data is very large, we construct a grouped frequency distribution table of class size 5.
∴, class intervals will be 0-5, 5-10, 10-15, 15-20 and so on. The data is represented in the grouped frequency distribution table as

Distance (in km)

Tally Marks 

No of Engineers
(Frequency)
0-5 5
5-10 | 11
10-15 | 11
15-20 |||| 9
20-25 | 1
25-30 | 1
30-35 || 2
Total 40

The following features can be observed from the above table.

  • 5 Engineers have their houses below 5 km.
  • A majority of engineers (31) have their houses below 20 km
  • Only a few engineers (4) have their houses at 20 km and above distance.

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

(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?

Answer – By drawing a frequency distribution table, we can observe data.
(i) Let construct a grouped frequency distribution table with a class size of 2.
The relation humidity (in %) of a certain city for a month can be represented as follows:

Relative humidity (in %) Frequency
84 – 86 1
86 – 88 1
88 – 90 2
90 – 92 2
92 – 94 7
94 – 96 6
96 – 98 7
98 – 100 4
Total 30

(ii) The following features can be observed from the above table:

  • The relative humidity was 92% and above, over a period of 24 days (four-fifth of a month)
  • Since the relative humidity % is very high, it must be data from a month of the rainy season or monsoon such as July or August.

(iii) Range of data = maximum value – minimum value
= 99.2 – 84.9
= 14.3

4. The heights of 50 students, measured to the nearest centimetres, 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 the class intervals as 160 – 165, 165 – 170, etc.
(ii) What can you conclude about their heights from the table?

Answer –
(i) The data given in the question can be represented by a grouped frequency distribution table, taking the class intervals as 160 – 165, 165 – 170, etc., as

Height (in cm) No. of Students
(Frequency)
150 – 155 12
155 – 160 9
160 – 165 14
165 – 170 10
170 – 175 5
Total 50

(ii) The following conclusions can be drawn from the table:

  • 70% of the students (35 students) are below 165 cm.
  • Only 10% of the students (5 students) are of height of 170 cm or more.

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?

Answer –
(i) A grouped frequency distribution table with a class size of ‘0.04’ needs to be constructed for the given data.

Concentration of sulphur dioxide in the air
(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 number of days in which the concentration of sulphur dioxide was more than 0.11 parts per million = 2 + 4 +  2 = 8

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.

Answer – The frequency distribution table for the data given in the question is given below.

Number of Heads Frequency
0 6
1 10
2 9
3 5
Total 30

7. The value of π up to 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?

Answer –
(i) The frequency distribution of the digits from 0 to 9 after the decimal point is given in the 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

(ii) It can be easily observed from the table that

  • The most frequently occurring digits are 3 and 9, with a max frequency of 8.
  • The least frequently occurring digit is ‘0’ with the lowest frequency of 2.

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 5 – 10.
(ii) How many children watch television for 15 or more hours a week?

Answer –
(i) The grouped frequency distribution table for the data given in the question, taking class width 5 and one of the class intervals 5-10, is given below.

Number of Hours Frequency
0 – 5 10
5 – 10 13
10 – 15 5
15 – 20 2
Total 30

(ii) We can observe from the table that the number of children who watched television for 15 or more hours a week is 2 (which falls under the class interval ‘15-20’).

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 interval 2 – 2.5.

Answer – The grouped frequency distribution table for the data given in the table, using class intervals of size 0.5 starting from interval 2 – 2.5, is given below.

Lives of batteries
(in years)		 No. of batteries
(Frequency)
2 – 2.5 2
2.5 – 3 6
3 – 3.5 14
3.5 – 4 11
4 – 4.5 4
4.5 – 5 3
Total 40

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