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Class 9 NCERT Solutions- Chapter 14 Statistics – Exercise 14.2

  • Last Updated : 13 Jan, 2021

Problem 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.

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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:



Frequency:- No. of students having the same blood group.

Blood GroupNo. of Students
A9
B6
AB3
O12
Total30

Most common blood group (highest frequency blood group) :- O

Rarest blood group (least frequency blood group) :- AB.

Problem 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:



Grouped frequency distribution table of class size 5:

Distance (in Kms)Frequency
0-55
5-1011
10-1511
15-209
20-251
25-301
30-352
Total40

We observe that, most of the engineers live within 20 kms from their place of work. Only 4 employees out of 40 employees are living in between 20 and 35 kms from their place of work.

Problem 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?

Solution:

(i) grouped frequency distribution table with classes 84 – 86, 86 – 88, etc….



Relative humidity (in %)Frequency
84-861
86-881
88-902
90-922
92-947
94-966
96-987
98-1004
Total30

(ii) In the most of days the humidity is very high, so this data should be from rainy season.

(iii) range of the data = maximum value in the data – minimum value in the data

                                  = 99.2 – 84.9

                                  = 14.3

Problem 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? 

Solution:

(i) grouped frequency distribution table with classes 160 – 165, 165 – 170, etc…

Height (in cm)Frequency
150-15512
155-1609
160-16514
165-17010
170-1755
Total50

(ii) from the above table we can tell that height of most of the students (35 students) is less than 165 cms.

Problem 5: A study was conducted to find out the concentration of sulphur dioxide in the air in

2020-21 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? 

Solution:

(i) grouped frequency distribution table with classes 0.00 – 0.04, 0.04 – 0.08, etc..

Concentration of sulphur dioxide in air

(in ppm)

Frequency
0.00-0.044
0.04-0.089
0.08-0.129
0.12-0.162
0.16-0.204
0.20-0.242
Total30

(ii) concentration of sulphur dioxide was more than 0.11 parts per million for 8 days. ((2 + 4 + 2) days).

Problem 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:

Frequency distribution table:

No. of headsFrequency
06
110
29
35
Total30

Problem 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:

(i) frequency distribution table:-

DigitFrequency
02
15
25
38
44
55
64
74
85
98
Total50

(ii) most frequently occurring digits : 3 & 9 (both occurred 8 times)

     least frequently occurring digits : 0 (occurred only twice).

Problem 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) grouped frequency distribution table with class width 5 :

No. of hoursfrequency
0-510
5-1013
10-155
15-202
Total30

(ii) from the above table, we can tell that only 2 children watched television for 15 or more hours a week.

Problem 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:

Grouped frequency distribution table with class intervals of size 0.5 starting from the interval 2 – 2.5:

life of battery (in years)Frequency
2-2.52
2.5-36
3-3.514
3.5-411
4-4.54
4.5-53
Total40



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