Theory question 105
StatisticsThe table shows the distribution of the heights (cm) of 60 seedlings in a vegetable garden.
Heights (cm): 0.1 − 0.3, 0.4 − 0.6, 0.7 − 0.9, 1.0 − 1.4, 1.5 − 1.9, 2.0 − 2.2, 2.3 − 2.5
Frequency: 6, 9, 12, 15, 3, 6, 9
(a) Draw a histogram for the distribution. (b) Use the histogram to estimate the modal height of the seedlings.
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(a) Class boundaries (widths): 0.05–0.35 (0.3), 0.35–0.65 (0.3), 0.65–0.95 (0.3), 0.95–1.45 (0.5), 1.45–1.95 (0.5), 1.95–2.25 (0.3), 2.25–2.55 (0.3).
Widths differ, so plot frequency density (frequency per 0.1 cm): 2, 3, 4, 3, 0.6, 2, 3. Draw touching bars on the boundaries, label axes, state scale.
(b) Tallest bar: 0.65–0.95. Join its top corners to the adjacent bars' tops (both height 3) and read where the lines cross: mode ≈ 0.65 + ½ × 0.3 = 0.80 cm.
With unequal widths, plot frequency density, not frequency.