GCSE · Histograms

Interpreting histogramsExam-style questions

Getting information back out of a histogram — a frequency is an area, so part of a class is the matching proportion of a bar's area. Why that rests on values being spread evenly within a class (and is therefore an estimate), and how to read off a total, a mean, the median class, a range that cuts across class boundaries, and a comparison of two groups.

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

DifficultyAllLevel 2Level 3Level 4Level 5
  1. 1
    The histogram shows the ages of the people at a swimming pool one afternoon.204060800.20.40.60.811.21.41.6Age (years)Frequency density(a) Work out the total number of people at the pool. [2]

    (b) Estimate the number of people aged between 2525 and 4545. [2]

    (c) Which class interval contains the median age? [1]
    Level 4 · 5 marksTry it
  2. 2
    Every entrant in a crossword competition finished the crossword in less than one hour.

    The histogram shows information about the time, tt minutes, that each entrant took.

    The bar for the class 30<t≤4530 < t \le 45 has not been drawn.0102030405060Time (minutes)Frequency densityThe table gives the numbers of entrants in two of the classes.
    Time (tt minutes)Number of entrants
    25<t≤3025 < t \le 303636
    30<t≤4530 < t \le 454848
    (a) Complete the histogram.

    (2 marks)
    (b) Work out the number of people who entered the competition.

    (2 marks)
    Level 4 · 4 marksTry it
  3. 3
    Kemi grows some seedlings in a tray.

    She measures the height, in cm, of each seedling and shows her results in this histogram.246810121416182022241234567891011Height (cm)Frequency densityKemi chooses a seedling from the tray at random.

    Work out an estimate for the probability that this seedling has a height between 55 cm and 1313 cm.

    (4 marks)
    Level 4 · 4 marksTry it
  4. 4
    102030405060700.511.522.53Time (seconds)Frequency densityThe histogram gives information about the times, in seconds, taken by a group of students to solve a puzzle.

    Work out an estimate for the mean time taken.
    Level 4 · 4 marksTry it
  5. 5
    102030405060700.511.522.533.5Height (cm)Frequency densityThe histogram gives information about the heights, in centimetres, of the plants in a nursery.

    (a) Work out the total number of plants.

    (b) Write down the class interval that contains the median height.
    Level 4 · 4 marksTry it

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