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In this page we have *NCERT book Solutions for Class 9th Maths:statistics* for
EXERCISE 1 . Hope you like them and do not forget to like , social share
and comment at the end of the page.

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?

The number of students who have a certain type of blood group is called frequency of the blood group

The below Frequency distribution is prepared

Blood Group |
Frequency |

A |
9 |

B |
6 |

O |
12 |

AB |
3 |

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 |

It is given that a grouped frequency distribution table of class size 5 has to be constructed. Therefore, the class intervals will be 0 − 5, 5 − 10, 10 − 15, 15 −20…

By observing the data given as above, a grouped frequency distribution table can be constructed as follows.

Class (Distance) |
Frequency |

0-5 |
5 |

5-10 |
11 |

10-15 |
11 |

15-20 |
9 |

20-25 |
1 |

25-30 |
1 |

30-35 |
2 |

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 |

84 - 86, 86 - 88

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

(iii) What is the range of this data?

Class intervals will be as follows 84 - 86, 86 - 88, and 88 - 90... ...

Relative humidity |
Frequency in days |

84-86 |
1 |

86-88 |
1 |

88-90 |
2 |

90-92 |
2 |

92-94 |
7 |

94-96 |
6 |

96-98 |
7 |

98-100 |
4 |

= 99.2 - 84.9

= 14.3

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 |

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

Class intervals will be as follows 160 - 165, 165 - 170, etc.

Heights |
Frequency |

150-155 |
12 |

155-160 |
9 |

160-165 |
14 |

165-170 |
10 |

170-175 |
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 |
0.2 |

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

0.08 |
0.01 |
0.1 |
0.06 |
0.09 |
0.18 |

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

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

Frequency distribution

Interval |
Frequency |

.00-.04 |
4 |

.04-.08 |
9 |

.08 - .12 |
9 |

.12- .16 |
2 |

.16-.20 |
4 |

.20-.24 |
2 |

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 |

Frequency table

Number of heads |
Frequency |

0 |
6 |

1 |
10 |

2 |
9 |

3 |
5 |

The value of π up to50 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?

Digits |
Frequency |

0 |
2 |

1 |
5 |

2 |
5 |

3 |
8 |

4 |
4 |

5 |
5 |

6 |
4 |

7 |
4 |

8 |
5 |

9 |
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 |
7 |
14 |
12 |

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

i) Frequency table

Number of hours |
Frequency |

0-5 |
10 |

5-10 |
13 |

10-15 |
5 |

15-20 |
2 |

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

2.6 |
3 |
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 |
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 |

Frequency distribution

Lives of battery |
Number of batteries |

2-2.5 |
2 |

2.5 -3.0 |
6 |

3.0 – 3.5 |
14 |

3.5-4.0 |
11 |

4.0 -4.5 |
4 |

4.5 – 5.0 |
3 |

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