The table gives the distribution of marks of 60 candidates in a test.
| Marks | 23-25 | 26-28 | 29-31 | 32-34 | 35-37 | 38-40 |
| Frequency | 3 | 7 | 15 | 21 | 10 | 4 |
(a) Draw a cumulative frequency curve of the distribution.
(b) From your curve, estimate the : (i) 80th percentile ; (ii) median ; (iii) semi-interquartile range.
Explanation
| Marks | Freq | Class Boundaries | Cum. Freq |
| 23 – 25 | 3 | 22.5 – 25.5 | 3 |
| 26 – 28 | 7 | 25.5 – 28.5 | 10 |
| 29 – 31 | 15 | 28.5 – 31.5 | 25 |
| 32 – 34 | 21 | 31.5 – 34.5 | 46 |
| 35 – 37 | 10 | 34.5 – 37.5 | 56 |
| 38 – 40 | 4 | 37.5 – 40.5 | 60 |
(a)
(b)(i) 80th percentile = (frac{80 times 60th}{100} = text{48th mark}).
= 31.5.
(ii) Median = (frac{60th}{2} = text{30th mark} = 32.3)
(iii) Upper quartile = (frac{3 times 60th}{4} = text{45th mark} = 35.1)
Lower quartile = (frac{60th}{4} = text{15th mark} = 29.7)
Semi-interquartile range = (frac{35.1 – 29.7}{2} = 2.7)