[discia] GCSE Maths › Statistics › Histograms

Histograms

discia.org 10 questions · 33 marks
Name Date
  1. Calculator 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.

    00.511.522.533.5frequency density010203040506070height (cm)
    (a)

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

    (b)

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

    Show answer
    (a) \(0.5\)
    (b) \(3\)
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  2. Calculator 2 marks

    The table shows information about the lengths of 135 journeys.

    Length (km)Frequency
    \(0 < d \le 10\)20
    \(10 < d \le 20\)15
    \(20 < d \le 40\)60
    \(40 < d \le 60\)40

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

    00.511.522.53frequency density0102030405060length of journey (km)

    Complete the histogram.

    Show answer
    The bar for \(10 < d \le 20\) drawn to \(1.5\) and the bar for \(40 < d \le 60\) drawn to \(2\)
    00.511.522.53frequency density0102030405060length of journey (km)
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  3. Calculator 4 marks

    The histogram gives information about the ages of some members of a sports club.

    00.511.522.5frequency density01020304050607080age (years)
    (a)

    Work out the number of members of a sports club whose age was between \(40\) and \(60\) years.

    (b)

    Work out the total number of members of a sports club.

    Show answer
    (a) \(40\)
    (b) \(155\)
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  4. Calculator 3 marks

    The histogram gives information about the durations (\(c\) minutes) of some phone calls.

    00.511.522.533.5frequency density0102030405060708090100call duration (minutes)
    (a)

    Which class contains the most phone calls? Show working to explain your answer.

    (b)

    Calculate how many more phone calls are in the class you found in part (a) than in the class \(80 < c \le 100\) minutes.

    Show answer
    (a) \(50 < c \le 80\) minutes
    (b) \(20\)
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  5. Calculator 4 marks

    The incomplete histogram and the incomplete table give information about the lengths of some journeys.

    Length (km)Frequency
    \(10 < d \le 20\)?
    \(20 < d \le 26\)?
    \(26 < d \le 38\)42
    \(38 < d \le 58\)90
    00.511.522.533.544.5frequency density1015202530354045505560length of journey (km)
    (a)

    Find the frequency for the class \(10 < d \le 20\).

    (b)

    Find the frequency for the class \(20 < d \le 26\).

    (c)

    The bar for the class \(26 < d \le 38\) is missing from the histogram. Draw the missing bar on the grid.

    Show answer
    (a) \(45\)
    (b) \(21\)
    (c) The bar for \(26 < d \le 38\) drawn to a height of \(3.5\)
    (c)00.511.522.533.544.5frequency density1015202530354045505560length of journey (km)
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  6. Calculator 3 marks

    The table shows information about the lengths of 130 phone calls.

    Length (seconds)Frequency
    \(50 < t \le 80\)60
    \(80 < t \le 100\)50
    \(100 < t \le 110\)10
    \(110 < t \le 130\)10

    One bar of the histogram has been drawn.

    00.511.522.5frequency density5060708090100110120130length of call (seconds)

    Complete the histogram.

    Show answer
    Bars of height \(2\), \(2.5\), \(1\) and \(0.5\) for the four classes in order, one of them already drawn
    00.511.522.5frequency density5060708090100110120130length of call (seconds)
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  7. Calculator 4 marks

    The histogram gives information about the times of some visitors.

    00.511.52frequency density0102030405060708090100time in museum (minutes)

    Two of the frequencies are missing from the table.

    Time in the museum (minutes)Frequency
    \(0 < t \le 20\)10
    \(20 < t \le 30\)
    \(30 < t \le 40\)10
    \(40 < t \le 60\)
    \(60 < t \le 100\)60
    (a)

    Use the histogram to work out the frequency for \(20 < t \le 30\).

    (b)

    Find the total number of visitors.

    Show answer
    (a) \(10\)
    (b) \(130\)
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  8. Calculator 3 marks

    The histogram gives information about the lengths of stay of 155 visitors to a museum.

    One of the bars has not been drawn.

    00.511.522.53frequency density0102030405060length of stay (minutes)

    Calculate the frequency density of the missing bar.

    Show answer
    \(1.5\)
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  9. Calculator 3 marks

    The histogram gives information about the charging times of some phones.

    00.511.522.533.5frequency density05101520253035404550charging time (minutes)

    The number of phones with a charging time between \(30\) and \(50\) minutes is the same as the number with a charging time between \(50\) and \(60\) minutes.

    The frequency density of this last class is \(x\).

    Calculate the value of \(x\).

    Show answer
    \(3\)
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  10. Calculator 3 marks

    The histogram gives information about the heights of 145 trees.

    00.511.522.533.5frequency density010203040506070height (metres)

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

    Show answer
    \(45\)
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discia.org Histograms · sheet 1
Answers Histograms · sheet 1
  1. (a) \(0.5\)
    (b) \(3\)
  2. The bar for \(10 < d \le 20\) drawn to \(1.5\) and the bar for \(40 < d \le 60\) drawn to \(2\)
    00.511.522.53frequency density0102030405060length of journey (km)
  3. (a) \(40\)
    (b) \(155\)
  4. (a) \(50 < c \le 80\) minutes
    (b) \(20\)
  5. (a) \(45\)
    (b) \(21\)
    (c) The bar for \(26 < d \le 38\) drawn to a height of \(3.5\)
    (c)00.511.522.533.544.5frequency density1015202530354045505560length of journey (km)
  6. Bars of height \(2\), \(2.5\), \(1\) and \(0.5\) for the four classes in order, one of them already drawn
    00.511.522.5frequency density5060708090100110120130length of call (seconds)
  7. (a) \(10\)
    (b) \(130\)
  8. \(1.5\)
  9. \(3\)
  10. \(45\)
discia.org Histograms · sheet 1