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					Worksheet – Representing Data – Histograms
1. James records the time he waits for a bus at his bus stop. The results are:
   Time, t, minutes      Frequency
      0< t≤2                  2
       2< t ≤ 4               4
      4 < t ≤ 10              9
     10 < t ≤ 20              3
Draw a histogram to represent these data.

2. A receptionist records the time taken for people to answer the phone when she calls them. Her
results are shown in the table.
   Time, t, seconds        Frequency
       0 < t ≤ 10               2
      10 < t ≤ 15               4
      15 < t ≤ 20               8
      20 < t ≤ 30               10
      30 < t ≤ 60               12
Draw a histogram for these data.

3. Seamus is measuring the lengths of leaves in a biology lesson. He records the results in the
following table.
     Length, l, cm        Frequency
        0<l≤2                  1
        2<l≤4                  4
        4<l≤5                  3
       5 < l ≤ 10              8
      10 < l ≤ 20              4
He draws the following histogram.




(a) What mistakes has Seamus made in his histogram?
(b) Draw a correct histogram for these data.
Worksheet – Representing Data – Histograms Answers

1.
     Time, t, minutes   Frequency   Class-width   Frequency
                                                    density
        0< t≤2             2            2           2/2 = 1
         2< t ≤ 4          4            2           4/2 = 2
        4 < t ≤ 10         9            6          9/6 = 1.5
       10 < t ≤ 20         3            10        3/10 = 0.3




2.
     Time, t, seconds   Frequency   Class-width   Frequency
                                                    density
        0 < t ≤ 10         2            10         2/10 = 0.2
       10 < t ≤ 15         4            5          4/5 = 0.8
       15 < t ≤ 20         8            5          8/5 = 1.6
       20 < t ≤ 30         10           10         10/10 = 1
       30 < t ≤ 60         12           30        12/30 = 0.4
3.
     (a)   The vertical axis is not labelled. Frequency has been used as the height of each rectangle
           instead of frequency density.
     (b)
      Length, l, cm       Frequency        Class-width       Frequency
                                                              density
        0<l≤2                  1                2               0.5
        2<l≤4                  4                2                2
        4<l≤5                  3                1                3
       5 < l ≤ 10              8                5               1.6
       10 < l ≤ 20             4                10              0.4

				
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posted:8/20/2010
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