2026-08-29T20:03:39.204767 image/svg+xml Matplotlib v3.10.9, https://matplotlib.org/ © EAGLE BEACON GLOBAL A delivery company records the number of parcels ...

A cumulative frequency graph is read by tracing across from a chosen cumulative frequency value on the vertical axis to the curve, then down to the horizontal axis; the median and quartiles are found this way at specific cumulative frequency values.

(a) With 68 shifts recorded for each route, the median lies at a cumulative frequency of \( 68 \div 2 = 34 \). Reading across from 34 on Route A's curve gives a median of about \( 27 \) parcels; doing the same on Route B's curve gives a median of about \( 35 \) to \( 36 \) parcels [2 marks].

(b) The lower quartile is read at a cumulative frequency of \( 68 \div 4 = 17 \), and the upper quartile at \( 3 \times 17 = 51 \). For Route A, this gives a lower quartile of about \( 19 \) and an upper quartile of about \( 36 \), an interquartile range of about \( 17 \) parcels. For Route B, this gives a lower quartile of about \( 26 \) and an upper quartile of about \( 44 \), an interquartile range of about \( 18 \) to \( 19 \) parcels [2 marks].

(c) Route A has the smaller interquartile range (about 17, against about 18-19 for Route B), which means the middle half of Route A's shifts are packed into a narrower range of parcel counts. Route A is therefore the more consistent route [1 mark].

The interquartile range, not the full range, is used to judge consistency because it ignores the most extreme few shifts on either route and focuses on the typical spread of the middle 50% of shifts.