The cumulative frequency graph below shows the weight of 240 students in a school. Use the graph to find

  1. (a)

    the number of students with a weight greater than 55 kg.

    Answer ...

  2. (b)

    the interquartile range.

    Answer ... kg

  3. (c)

    the median.

    Answer ... kg

  4. (d)

    It was discovered that the weighing machine used to measure the weight of the students was faulty.

    The weight of each of the students was supposed to be 5 kg more than their recorded weights.

    (d) Explain how the cumulative frequency curve of the corrected weights will differ from the given curve.

    Answer ...

    ...

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Worked solution

24(a)

1. Find the number of students with weight greater than 55 kg

From the cumulative frequency graph, the number of students with weight ≤55\leq 55 kg is approximately 238238.

Total number of students =240=240.

Number with weight >55>55 kg:
240−238=2240-238=2

Answer

22 students

24(d)

1. Identify the effect of adding 5 kg to every recorded weight

Each corrected weight is
recorded weight+5\text{recorded weight} + 5 kg.

So a student recorded at weight xx kg will be shown at corrected weight (x+5)(x+5) kg.

2. Describe how the cumulative frequency curve changes

The number of students is unchanged, so the cumulative frequencies stay the same.

Only the horizontal weight values increase by 55 kg. Hence the curve is shifted 55 kg to the right, with the same shape.

Answer

The corrected cumulative frequency curve will have the same shape as the given curve, but translated 55 kg to the right. The cumulative frequencies remain unchanged.

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