One data set, three diagrams, the same story.

Sixty phone calls, grouped by length. A histogram, a cumulative frequency curve and a box plot are not three different things to learn — they are three views of these same sixty numbers.

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The classes are different widths, so the height is the frequency density and it is the area that counts. The 4–8 class holds 20 calls — more than any other — yet its bar is lower than its neighbour's, because it is twice as wide.

Now stack each bar on the total so far: 9, then 24, then 44, 54, 60. Each block still holds its own class, but its top edge is the number of calls shorter than that class's upper boundary.

Join those top corners and you have the cumulative frequency curve. Go in at half the total, $\tfrac{n}{2} = 30$, across to the curve and down: the median is 5.2 minutes. The quartiles come from 15 and 45 the same way.

Those three readings are the box: 2.8 to 8.4, median 5.2, $\text{IQR} = 5.6$. A whisker runs down to the shortest call, 0.4.

Past $8.4 + 1.5 \times 5.6 = 16.8$ is an outlier: the 19-minute call gets its own cross, and the upper whisker stops at the fence.

Same data. Pick the view that answers your question.

Drawing histograms with awkward scales, reading percentiles off a curve, outlier rules, cleaning data, comparing distributions, and twelve graded exam questions with full worked solutions are waiting.

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