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".

Start practising Read the lesson

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    A histogram is drawn to represent a set of values of tt. It has exactly three bars.
    ClassFrequency density
    0<t≤80 < t \le 82.5
    8<t≤208 < t \le 204.5
    20<t≤k20 < t \le k1.2
    The bar for the class 20<t≤k20 < t \le k represents 30 values.

    (a) Work out the value of kk.

    (b) Work out the total number of values represented by the histogram.
    Level 5 · 6 marksTry it
  2. 2
    A histogram showing the masses, mm grams, of some parcels is drawn on squared paper. There is no scale on the frequency density axis.

    The bar for the class 0<m≤200 < m \le 20 is 44 cm wide and 33 cm high, and it represents 24 parcels.

    (a) The bar for the class 20<m≤3020 < m \le 30 is 22 cm wide and 4.54.5 cm high. Work out the number of parcels it represents.

    (b) The class 30<m≤4530 < m \le 45 contains 45 parcels. Its bar is 33 cm wide. Work out the height of that bar.
    Level 5 · 6 marksTry it