GCSE · Histograms

Histograms & frequency densityExam-style questions

Why a histogram with unequal class widths cannot use frequency as the bar height, and how the rule "area = frequency" fixes it: height = frequency ÷ class width. Drawing the bars, reading a frequency back off a bar as density × width, and why the axis must say "Frequency density".

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10 questions · GCSE (Higher) level · mark scheme and worked solution on each · no sign-up to try

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    The times, tt minutes, that 100 customers spent in a shop were recorded and shown on a histogram. The histogram below is incomplete: the bar for the class 20<t≤3020 < t \le 30 has not been drawn.1020304050600.511.522.53Time, t (minutes)Frequency density(a) Work out the number of customers who spent between 2020 and 3030 minutes in the shop.

    (b) Work out the height of the bar that should be drawn for the class 20<t≤3020 < t \le 30.
    Level 4 · 4 marksTry it
  2. 2
    The lengths of 84 nails were each measured to the nearest millimetre. The results are shown in the table.
    Length (mm)Frequency
    20–2416
    25–2924
    30–3930
    40–5914
    (a) Explain why the class 25–29 has a class width of 5 and not 4.

    (b) Work out the frequency density of each of the four classes.
    Level 4 · 4 marksTry it
  3. 3
    Chloe timed each of 65 people answering a question. Her results are in the table.
    Time, ss (seconds)Frequency
    0<s≤100 < s \le 1012
    10<s≤1510 < s \le 1518
    15<s≤2015 < s \le 2015
    20<s≤4020 < s \le 4020
    She then drew the chart below, using the frequency of each class as the height of its bar.102030405101520Time, s (seconds)Frequency (Chloe's heights)Chloe says, "My chart shows that the 20<s≤4020 < s \le 40 group is the busiest."

    (a) Explain why Chloe's chart is misleading.

    (b) Work out the correct height of each bar for a histogram of this data.
    Level 4 · 4 marksTry it