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

- (a)
the number of students with a weight greater than 55 kg.
Answer ...
- (b)
the interquartile range.
Answer ... kg
- (c)
the median.
Answer ... kg
- (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 kg is approximately .
Total number of students .
Number with weight kg:
students
24(d)
1. Identify the effect of adding 5 kg to every recorded weight
Each corrected weight is
kg.
So a student recorded at weight kg will be shown at corrected weight 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 kg. Hence the curve is shifted kg to the right, with the same shape.
The corrected cumulative frequency curve will have the same shape as the given curve, but translated kg to the right. The cumulative frequencies remain unchanged.
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