Theory question 105
StatisticsThe table shows the distribution of monthly income (in thousands of naira) of workers in a factory.
Monthly Income (₦'000): 135−139, 140−149, 150−154, 155−164, 165−169
Number of workers: 20, 42, 28, 38, 22
(a) Draw a histogram for the distribution. (b) Use your graph to estimate the mode of the distribution.
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(a) Boundaries (widths): 134.5–139.5 (5), 139.5–149.5 (10), 149.5–154.5 (5), 154.5–164.5 (10), 164.5–169.5 (5).
Unequal widths: plot frequency per 5 (₦'000) – heights 20, 21, 28, 19, 22 – as touching bars on the boundaries.
(b) Tallest bar 149.5–154.5. Cross lines from its top corners to the neighbouring bars (21 and 19): mode ≈ 149.5 + 5 × 7/(7 + 9) ≈ 151.7, i.e. about ₦151 700.
With unequal class widths, bar heights must be frequency densities.