The table shows the heights in cm of some seedlings in a certain garden.
| Height (cm) | 36-40 | 41-45 | 46-50 | 51-55 | 56-60 |
| Frequency | 3 | 9 | 21 | 12 | 5 |
(a) Draw the cumulative frequency curve for the distribution.
(b) Using the curve in (a), find thesemi-interquartile range.
Explanation
| Height (cm) | Freq | Class boundaries | Cum. freq |
| 36 – 40 | 3 | 35.5 – 40.5 | 3 |
| 41 – 45 | 9 | 40.5 – 45.5 | 12 |
| 46 – 50 | 21 | 45.5 – 50.5 | 33 |
| 51 – 55 | 12 | 50.5 – 55.5 | 45 |
| 56 – 60 | 5 | 55.5 – 60.5 | 50 |
(a)
(b) Lower quartile (Q_{1}) = 45.6cm
Upper quartile (Q_{3}) = 52.0cm
Semi- interquartile range = (frac{Q_{3} – Q_{1}}{2})
= (frac{52 – 45.6}{2})
= (frac{6.4}{2})
= (3.2cm)