Chapter 14 Statistics Exercise 14.2
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?
Answer:
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?
Answer:
• Frequencies of class intervals 5 - 10 and 10 - 15 are equal, i.e., 11 each. It shows that maximum number of engineers have their residences at 5 to 15 km away from their work place.
• Frequencies of class intervals 20 - 25 and 25 - 30 are also equal, i.e., 1 each. It shows that minimum number of engineers have their residences at 20 to 30 km away from their work place.
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 |
(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:
iii) Range = Highest observation - Lowest observation
Range = 99.2 – 84.9
= 14.3
Question 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) As the lowest observation is 150 therefore we will start the class intervals with 150 i.e. 150 - 155.
As the highest observation is 173 therefore we will end the class intervals with 175 i.e. 170 - 175.
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?
Answer:
i)
ii) The concentration of sulphur dioxide was more than 0.11 ppm for 8 days.
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.
Answer:
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?
Answer:
i)ii) The most frequently occurring digits are 3 and 9 while 0 is the least frequently occurring digit.
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?
Answer:
i)
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.
Answer:
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