3. The numbers of people travelling on a certain bus at different times of the day are has follows. 17 5 2 23 16 31 8 22 14 25 35 17 27 12 6 23 19 21 23 8 26 (i) Draw a frequency distribution table to illustrate the information given above. Use intervals 00-04, 05-09; 10-14, 15-19, ... [15 marks] (ii) Find the median, [10 marks] (iii) the lower quartile, [10 marks] (iv) the upper quartile, [10 marks] (v) and the interquartile range
Question
- The numbers of people travelling on a certain bus at different times of the day are has follows. 17 5 2 23 16 31 8 22 14 25 35 17 27 12 6 23 19 21 23 8 26
(i) Draw a frequency distribution table to illustrate the information given above. Use intervals 00-04, 05-09; 10-14, 15-19, ... [15 marks] (ii) Find the median, [10 marks] (iii) the lower quartile, [10 marks] (iv) the upper quartile, [10 marks] (v) and the interquartile range
Solution
(i) Frequency Distribution Table:
| Interval | Frequency |
|---|---|
| 00-04 | 1 |
| 05-09 | 4 |
| 10-14 | 3 |
| 15-19 | 5 |
| 20-24 | 7 |
| 25-29 | 4 |
| 30-34 | 1 |
| 35-39 | 1 |
(ii) Median:
First, arrange the numbers in ascending order: 2, 5, 6, 8, 8, 12, 14, 16, 17, 17, 19, 21, 22, 23, 23, 23, 25, 26, 27, 31, 35
The median is the middle number. Since there are 21 numbers, the median is the 11th number, which is 19.
(iii) Lower Quartile (Q1):
The lower quartile is the median of the first half of the data. Since there are 21 numbers, the first half is the first 10 numbers. The median of these 10 numbers is the average of the 5th and 6th numbers, which is (8+8)/2 = 8.
(iv) Upper Quartile (Q3):
The upper quartile is the median of the second half of the data. Since there are 21 numbers, the second half is the last 10 numbers. The median of these 10 numbers is the average of the 5th and 6th numbers, which is (23+23)/2 = 23.
(v) Interquartile Range:
The interquartile range is the difference between the upper quartile and the lower quartile. So, the interquartile range is Q3 - Q1 = 23 - 8 = 15.
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