Discia GCSE Maths › Statistics › Histograms

Histograms worksheet

10 GCSE practice questions with answers, free to print. Every sheet is generated, so you can make a fresh one whenever you need it.

10 questions 39 marks Sheet 1
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  1. 4 marks

    The table gives information about the heights of 190 plants.

    Height (cm)Frequency
    \(0 < h \le 10\)35
    \(10 < h \le 20\)5
    \(20 < h \le 50\)90
    \(50 < h \le 70\)60

    The histogram has been started. Two of the bars are missing.

    A partly drawn histogram: two bars are drawn and two are missing00.511.522.533.5frequency density010203040506070height (cm)
    (a)

    Find the frequency density of the bar for \(10 < h \le 20\).

    (b)

    Find the frequency density of the bar for \(50 < h \le 70\).

  2. 4 marks

    The histogram gives information about the speeds of some cars.

    A histogram with four bars of unequal width and frequency density up the vertical axis00.511.522.533.5frequency density010203040506070speed (mph)
    (a)

    Work out the number of cars whose speed was between \(20\) and \(50\) mph.

    (b)

    Work out the total number of cars.

  3. 4 marks

    The histogram gives information about the lifetimes of some batteries.

    A histogram with five bars of unequal width and frequency density up the vertical axis00.511.522.53frequency density0102030405060708090lifetime (hours)

    Two of the frequencies are missing from the table.

    Lifetime (hours)Frequency
    \(0 < t \le 20\)30
    \(20 < t \le 40\)
    \(40 < t \le 50\)20
    \(50 < t \le 70\)
    \(70 < t \le 90\)10
    (a)

    Use the histogram to work out the frequency for \(20 < t \le 40\).

    (b)

    Calculate the total number of batteries.

  4. 3 marks

    The histogram gives information about the heights of 120 trees.

    A histogram with four bars of unequal width and frequency density up the vertical axis00.511.52frequency density010203040506070height (metres)

    Estimate the number of trees whose height was between \(20\) and \(40\) metres.

  5. 3 marks

    The histogram gives information about the heights of 120 shrubs.

    A histogram with four bars of unequal width and frequency density up the vertical axis00.511.522.533.5frequency density010203040506070height (cm)

    Use the histogram to estimate the median height.

  6. 5 marks

    The histogram gives information about the times of 155 swimmers.

    A histogram with four bars of unequal width and frequency density up the vertical axis00.511.522.53frequency density0102030405060time (seconds)
    (a)

    Estimate the number of swimmers whose time was more than \(20\) seconds.

    (b)

    One of the swimmers is chosen at random.

    Estimate the probability that its time was more than \(20\) seconds. Give your answer as a fraction in its simplest form.

  7. 4 marks

    The histogram gives information about the times of some pupils.

    There are no numbers on the frequency density axis.

    A histogram with four bars of unequal width, drawn on a gridded vertical axis with no numbers on itfrequency density010203040506070time reading (minutes)

    20 pupils had a time spent reading between \(0\) and \(10\) minutes.

    (a)

    Find the number of pupils whose time spent reading was between \(10\) and \(30\) minutes.

    (b)

    Find the total number of pupils.

  8. 4 marks

    The table gives information about the heights of 80 plants.

    Height (cm)Frequency
    \(0 < h \le 10\)10
    \(10 < h \le 20\)10
    \(20 < h \le 40\)30
    \(40 < h \le 60\)30

    The histogram has been started. Two of the bars are missing.

    A partly drawn histogram: two bars are drawn and two are missing00.511.5frequency density0102030405060height (cm)
    (a)

    Find the frequency density of the bar for \(10 < h \le 20\).

    (b)

    Find the frequency density of the bar for \(40 < h \le 60\).

  9. 4 marks

    The histogram gives information about the lengths of some phone calls.

    A histogram with four bars of unequal width and frequency density up the vertical axis00.511.522.53frequency density010203040506070length of call (minutes)
    (a)

    Calculate the number of phone calls whose length was between \(30\) and \(50\) minutes.

    (b)

    Calculate the total number of phone calls.

  10. 4 marks

    The histogram gives information about the heights of some seedlings.

    A histogram with five bars of unequal width and frequency density up the vertical axis00.511.522.533.5frequency density0102030405060708090height (mm)

    Two of the frequencies are missing from the table.

    Height (mm)Frequency
    \(0 < h \le 20\)60
    \(20 < h \le 40\)
    \(40 < h \le 50\)35
    \(50 < h \le 70\)
    \(70 < h \le 90\)10
    (a)

    Use the histogram to work out the frequency for \(20 < h \le 40\).

    (b)

    Calculate the total number of seedlings.

Answers

  1. (a) \(0.5\)
    (b) \(3\)
  2. (a) \(45\)
    (b) \(130\)
  3. (a) \(60\)
    (b) \(170\)
  4. \(35\)
  5. \(30\ \text{cm}\)
  6. (a) \(100\)
    (b) \(\frac{20}{31}\)
  7. (a) \(10\)
    (b) \(90\)
  8. (a) \(1\)
    (b) \(1.5\)
  9. (a) \(50\)
    (b) \(160\)
  10. (a) \(60\)
    (b) \(185\)

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