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 table shows information about the masses, mm kilograms, of 70 suitcases checked in at an airport desk.
    Mass, mm (kg)Frequency
    0<m≤200 < m \le 2036
    20<m≤3020 < m \le 3022
    30<m≤6030 < m \le 6012
    (a) Work out the frequency density of each class.

    (b) Ravi says, "The class 0<m≤200 < m \le 20 must have the tallest bar on the histogram, because it has the largest frequency."

    Is Ravi correct? Explain your answer.
    Level 2 · 3 marksTry it
  2. 2
    The table shows the ages of 4444 people at a club.
    Age, aa (years)Frequency
    0<a≤100 < a \le 108
    10<a≤1510 < a \le 1512
    15<a≤2515 < a \le 2515
    25<a≤4025 < a \le 409
    (a) Work out the frequency density for the 15<a≤2515 < a \le 25 class. (1 mark)

    (b) Estimate the number of people older than 2020. (2 marks)
    Level 3 · 3 marksTry it
  3. 3
    The table shows the lengths, ll cm, of 6262 fish.
    Length, ll (cm)Frequency
    0<l≤50 < l \le 510
    5<l≤155 < l \le 1524
    15<l≤2015 < l \le 2012
    20<l≤4020 < l \le 4016
    (a) Work out the frequency density of the 5<l≤155 < l \le 15 class. [1]

    (b) Estimate the number of fish with lengths between 1010 cm and 2020 cm. [2]
    Level 3 · 3 marksTry it
  4. 4
    The histogram shows information about the weights, ww grams, of the letters posted at a post box one morning.204060801001234Weight, w (grams)Frequency density(a) Work out the number of letters that weighed more than 6060 g.

    (b) Work out the total number of letters posted.
    Level 3 · 5 marksTry it
  5. 5
    The table shows information about the distances, dd metres, thrown by each of 100 competitors at a school sports day.
    Distance, dd (m)Frequency
    0≤d<100 \le d < 1020
    10≤d<2510 \le d < 2545
    25≤d<3025 \le d < 3020
    30≤d<5030 \le d < 5015
    (a) Draw a histogram for this information.

    (b) Explain why the vertical axis of your histogram must be labelled "Frequency density" and not "Frequency".
    Level 3 · 4 marksTry it

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