2026-08-29T20:03:40.122974 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL The histogram shows repair times, in minutes, for...
Question 1 Report
The histogram shows repair times, in minutes, for \(60\) bikes serviced at Wheelworks bicycle repair shop last week, grouped into equal \(10\)-minute classes. The bar for the \(20\)-\(30\) class is missing from the histogram.
- Work out the frequency for the \(20\)-\(30\) class. (2)
- State the height of the missing bar, given that the classes are of equal width. (1)
Answer Details
When every class in a grouped frequency table must add to a known total, a single missing frequency is found by subtracting the sum of the known frequencies from that total; for equal class widths, frequency density and frequency are then simply equal.
(a) Reading the four known frequencies from the histogram (8, 16, 14 and 6) and adding them: \( 8+16+14+6=44 \). Since the total number of bikes is 60, the missing frequency is \( 60-44=16 \) [2 marks].
(b) Frequency density is frequency divided by class width; since every class here has the same width of 10 minutes, the frequency density (and therefore the bar's height on this histogram) is numerically equal to the frequency itself, \( 16 \) [1 mark].
This equal-height-equals-frequency shortcut only works because every class in this table has the same width; if one class were wider or narrower than the rest, its bar height would have to be its frequency divided by that class's own width, not the frequency itself.
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