The cumulative frequency diagram shows the time in hours that each of the 120 adults from Town A spend on exercise in one week.

  1. (a)

    Explain if you can find the probability of an adult spending exactly 5 hours on exercise weekly.

    ...

  2. (b)

    The health promotion board recommends at least k hours of weekly exercise for adults to stay fit and active. 60 % of the adults in Town A meet this recommended weekly exercise hours. Find the value of k.

    Answer k = ...

  3. (c)

    Find the median and interquartile range of the weekly exercise hours of the adults in Town B.

    Answer Median = ... h

        Interquartile range = ...… h
  4. (d)

    Make two comparisons between the weekly exercise hours of the adults from Town A and Town B. State your reasons.

Analysis interpretationMeasure of chanceQuartiles percentilesMeasures of spread中文
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Worked solution

24(a)

1. Explain why the exact probability cannot be found from the graph

The diagram is a cumulative frequency graph for time spent on exercise, which is treated as continuous data. It can show how many adults spent up to a certain time, but it does not show the frequency for exactly one value such as exactly 55 hours.

Answer

No. The cumulative frequency graph shows cumulative values for intervals, so it cannot give the probability of spending exactly 55 hours.

24(c)

1. Read the median and quartiles from the box-and-whisker plot

From the box-and-whisker plot for Town B,

Q1=2Q_1 = 2 h, median =3= 3 h, and Q3=6Q_3 = 6 h.

2. Calculate the interquartile range

Interquartile range

=Q3−Q1= Q_3 - Q_1

=6−2= 6 - 2

=4= 4 h.

Answer

Median =3= 3 h

Interquartile range =4= 4 h

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