Theory question 112
StatisticsThe table shows the distribution of heights of a group of people.
Height (m): 0.4 − 0.5, 0.6 − 0.9, 1.0 − 1.2, 1.3 − 1.4, 1.5 − 1.7
No. of People: 2, 8, 12, 6, 6
(a) Draw a histogram to illustrate the distribution. (b) Using an assumed mean of 1.1 m, find, correct to one decimal place, the mean height of the group.
Show the model answer
Model answer
(a) Boundaries (widths): 0.35–0.55 (0.2), 0.55–0.95 (0.4), 0.95–1.25 (0.3), 1.25–1.45 (0.2), 1.45–1.75 (0.3). Unequal widths: plot frequency per 0.1 m – 1, 2, 4, 3, 2 – as touching bars.
(b) Class marks 0.45, 0.75, 1.1, 1.35, 1.6; d = −0.65, −0.35, 0, 0.25, 0.5.
Σfd = −1.3 − 2.8 + 0 + 1.5 + 3.0 = 0.4; Σf = 34.
Mean = 1.1 + 0.4/34 ≈ 1.1 m.
Explanation
With unequal class widths, plot frequency densities.