- The stem lengths of a sample of 120 tulips are recorded in the grouped frequency table below.
| Stem length (cm) | Frequency |
| \(40 \leqslant x < 42\) | 12 |
| \(42 \leqslant x < 45\) | 18 |
| \(45 \leqslant x < 50\) | 23 |
| \(50 \leqslant x < 55\) | 35 |
| \(55 \leqslant x < 58\) | 24 |
| \(58 \leqslant x < 60\) | 8 |
A histogram is drawn to represent these data.
The area of the bar representing the \(40 \leqslant x < 42\) class is \(16.5 \mathrm {~cm} ^ { 2 }\)
- Calculate the exact area of the bar representing the \(42 \leqslant x < 45\) class.
The height of the tallest bar in the histogram is 10 cm .
- Find the exact height of the second tallest bar.
\(Q _ { 1 }\) for these data is 45 cm . - Use linear interpolation to find an estimate for
- \(Q _ { 2 }\)
- the interquartile range.
One measure of skewness is given by
$$\frac { Q _ { 3 } - 2 Q _ { 2 } + Q _ { 1 } } { Q _ { 3 } - Q _ { 1 } }$$
- By calculating this measure, describe the skewness of these data.