The cumulative frequency graph shows the distribution of heights of a sample of 240 children from ABC Primary School.

  1. (a)

    Find the interquartile range.

    Answer ... cm

  2. (b)

    It is given that 15% of the students are taller than h cm.

    Find the value of h.

    Answer h = ...

  3. (c)

    The height of 240 children from XYZ Primary School have a larger median and a smaller standard deviation.

    Describe how their cumulative frequency curve will differ from ABC Primary School.

    Answer ...

    ...

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Worked solution

22(c)

1. Relate the larger median to the position of the cumulative frequency curve.

For both schools, there are 240240 children, so the median is read at cumulative frequency
2402=120.\frac{240}{2}=120.
A larger median means that, at cumulative frequency 120120, the height for XYZ is greater than that for ABC. Hence the XYZ curve is further to the right.

2. Relate the smaller standard deviation to the spread and steepness of the curve.

A smaller standard deviation means the heights are less spread out about the median. On a cumulative frequency curve, less spread gives a more compressed horizontal distribution, so the curve is steeper.

Answer

The cumulative frequency curve for XYZ will be shifted to the right of ABC’s curve and will be steeper, showing less spread.

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