[discia] GCSE Maths › Probability › Frequency Polygons

Frequency Polygons

discia.org 10 questions · 30 marks
Name Date
  1. Either paper 3 marks

    The frequency polygon shows the times of some shoppers.

    time in shop (minutes)frequency102030405060708090100510150
    (a)

    Write down the number of shoppers in the class \(20 < t \le 40\).

    (b)

    Find the total number of shoppers.

    Show answer
    (a) \(9\)
    (b) \(42\)
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  2. Either paper 3 marks

    The table gives information about the lengths of some fish.

    Length (cm)Frequency
    \(0 < L \le 10\)2
    \(10 < L \le 20\)10
    \(20 < L \le 30\)19
    \(30 < L \le 40\)9
    \(40 < L \le 50\)2

    A frequency polygon has been started. The first two points are plotted.

    length of fish (cm)frequency510152025303540455051015200
    (a)

    Write down the coordinates of the next point to plot.

    (b)

    Work out the total number of fish.

    Show answer
    (a) \((25, 19)\)
    (b) \(42\)
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  3. Either paper 4 marks

    33 Team A students and 33 Team B students each did a quiz.

    The frequency polygons show how long they took.

    time (minutes)frequency1020304050607080510150Team ATeam B
    (a)

    How many Team B students took between \(40\) and \(60\) minutes?

    (b)

    How many more Team A students than Team B students took between \(20\) and \(40\) minutes?

    (c)

    Which group generally took longer?

    Show answer
    (a) \(14\)
    (b) \(9\)
    (c) Team B
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  4. Either paper 3 marks

    The frequency polygon shows the times of 37 visitors.

    time in queue (minutes)frequency510152025303540455051015200
    (a)

    Write down the modal class.

    (b)

    Work out the number of visitors with a time in the queue of more than \(30\) minutes.

    Show answer
    (a) \(20 < t \le 30\)
    (b) \(7\)
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  5. Either paper 2 marks

    The table shows information about the time taken by some students to finish a puzzle.

    Time (\(t\) minutes)Frequency
    \(0 < t \le 20\)10
    \(20 < t \le 40\)14
    \(40 < t \le 60\)12
    \(60 < t \le 80\)18
    \(80 < t \le 100\)2

    On the grid, draw a frequency polygon for this information. Plot the five points and join them with straight lines. Do not extend the polygon to the horizontal axis.

    time (minutes)frequency102030405060708090100246810121416182022240
    Show answer
    Points at \((10, 10)\), \((30, 14)\), \((50, 12)\), \((70, 18)\) and \((90, 2)\), joined by straight lines
    time (minutes)frequency102030405060708090100246810121416182022240
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  6. Either paper 2 marks

    The table shows information about the lengths of some video calls.

    Length of call (\(L\) minutes)Frequency
    \(10 < L \le 30\)1
    \(30 < L \le 50\)1
    \(50 < L \le 70\)1
    \(70 < L \le 90\)3
    \(90 < L \le 110\)4
    \(110 < L \le 130\)4

    On the grid, draw a frequency polygon for the information in the table. Do not extend the polygon to the horizontal axis.

    length of call (minutes)frequency102030405060708090100110120130123456789100
    Show answer
    Points at \((20, 1)\), \((40, 1)\), \((60, 1)\), \((80, 3)\), \((100, 4)\) and \((120, 4)\), joined by straight lines
    length of call (minutes)frequency102030405060708090100110120130123456789100
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  7. Either paper 4 marks

    The frequency polygon shows the times of \(46\) students.

    time (minutes)frequency10203040506070809010051015200

    Each point is plotted at the middle of its class.

    (a)

    Write down the modal class.

    (b)

    Find an estimate for the mean time of the students.

    Show answer
    (a) \(40 < t \le 60\)
    (b) \(50\ \text{minutes}\)
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  8. Either paper 3 marks

    The table shows information about the lengths of 82 fish.

    Length (\(L\) cm)Frequency
    \(7 < L \le 17\)20
    \(17 < L \le 27\)17
    \(27 < L \le 37\)6
    \(37 < L \le 47\)16
    \(47 < L \le 57\)15
    \(57 < L \le 67\)8
    (a)

    Find the class interval that contains the median.

    (b)

    On the grid, draw a frequency polygon for the information in the table. Plot the six points and join them with straight lines. Do not extend the polygon to the horizontal axis.

    length (L cm)frequency612182430364248546066727824681012141618202224260
    Show answer
    (a) \(27 < L \le 37\)
    (b) Points at \((12, 20)\), \((22, 17)\), \((32, 6)\), \((42, 16)\), \((52, 15)\), \((62, 8)\), joined by straight lines
    (b)length (L cm)frequency612182430364248546066727824681012141618202224260
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  9. Either paper 3 marks

    The frequency polygon shows the times of some shoppers.

    time in shop (minutes)frequency10203040506070809010051015200
    (a)

    State the number of shoppers in the class \(80 < t \le 100\).

    (b)

    Work out the total number of shoppers.

    Show answer
    (a) \(3\)
    (b) \(48\)
    Another like this
  10. Either paper 3 marks

    The table shows information about the times of some students.

    Time (minutes)Frequency
    \(0 < t \le 10\)7
    \(10 < t \le 20\)13
    \(20 < t \le 30\)15
    \(30 < t \le 40\)3
    \(40 < t \le 50\)1

    A frequency polygon has been started. The first two points are plotted.

    time (minutes)frequency510152025303540455051015200
    (a)

    Write down the coordinates of the next point to plot.

    (b)

    Find the total number of students.

    Show answer
    (a) \((25, 15)\)
    (b) \(39\)
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discia.org Frequency Polygons · sheet 1
Answers Frequency Polygons · sheet 1
  1. (a) \(9\)
    (b) \(42\)
  2. (a) \((25, 19)\)
    (b) \(42\)
  3. (a) \(14\)
    (b) \(9\)
    (c) Team B
  4. (a) \(20 < t \le 30\)
    (b) \(7\)
  5. Points at \((10, 10)\), \((30, 14)\), \((50, 12)\), \((70, 18)\) and \((90, 2)\), joined by straight lines
    time (minutes)frequency102030405060708090100246810121416182022240
  6. Points at \((20, 1)\), \((40, 1)\), \((60, 1)\), \((80, 3)\), \((100, 4)\) and \((120, 4)\), joined by straight lines
    length of call (minutes)frequency102030405060708090100110120130123456789100
  7. (a) \(40 < t \le 60\)
    (b) \(50\ \text{minutes}\)
  8. (a) \(27 < L \le 37\)
    (b) Points at \((12, 20)\), \((22, 17)\), \((32, 6)\), \((42, 16)\), \((52, 15)\), \((62, 8)\), joined by straight lines
    (b)length (L cm)frequency612182430364248546066727824681012141618202224260
  9. (a) \(3\)
    (b) \(48\)
  10. (a) \((25, 15)\)
    (b) \(39\)
discia.org Frequency Polygons · sheet 1