Statistics
Exercise 14.2
Part 1
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:
| Blood Group | Number of Students |
|---|---|
| A | 9 |
| B | 6 |
| AB | 3 |
| O | 12 |
| Total | 30 |
- Most common blood group = O
- Rarest blood group = AB
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:
| Distance (in km) | Number of Engineers |
|---|---|
| 0 – 5 | 5 |
| 5 – 10 | 11 |
| 10 – 15 | 11 |
| 15 – 20 | 10 |
| 20 – 25 | 1 |
| 25 – 30 | 1 |
| 30 – 35 | 1 |
| Total | 40 |
- Most of the engineers live within 20 km.
- Very few live beyond 20 km.
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.
Answer:
| Relative Humidity | Number of 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 |
| Total | 30 |
(ii) Which month or season do you think this data is about?
Answer: Rainy season
(iii) What is the range of this data?
Answer:Range of data = 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.
Answer:
| Height | Number of Students |
|---|---|
| 150 – 155 | 12 |
| 155 – 160 | 9 |
| 160 – 165 | 14 |
| 165 – 170 | 10 |
| 170 – 175 | 5 |
| Total | 50 |
(ii) What can you conclude about their heights from the table?
Answer: Most of the students are 160 – 170 cm tall.
Very few students are taller than 170 cm.