The cumulative frequency graph shows the distances jumped, in metres, by 40 competitors in the long jump at a school sports day. 0 5 10 15 20 25 30 35 40 0 ...
Question 1 Report
The cumulative frequency graph shows the distances jumped, in metres, by 40 competitors in the long jump at a school sports day.
- Use the graph to find the median distance jumped. (1)
- Use the graph to find the interquartile range of the distances. (2)
- Use the graph to estimate the number of competitors who jumped further than 5.5 m. (1)
Answer Details
This question tests reading the median, the two quartiles and a specific cumulative frequency value directly from a cumulative frequency graph.
(a) With 40 competitors, the median lies at a cumulative frequency of \( 40 \div 2 = 20 \). Reading across from 20 on the vertical axis to the curve, then down to the horizontal axis, gives a median distance of 4.8 m (accept 4.6 to 5.0). [1 mark]
(b) The lower quartile is read at a cumulative frequency of \( 40 \div 4 = 10 \), giving 4.0 m, and the upper quartile is read at \( 3 \times 40 \div 4 = 30 \), giving 5.7 m. The interquartile range is
\[ 5.7 - 4.0 = 1.7 \text{ m (accept 1.5 to 1.9)} \] [2 marks]
(c) Reading up from 5.5 m on the horizontal axis to the curve gives a cumulative frequency of about 28, meaning 28 competitors jumped 5.5 m or less. The number who jumped further than 5.5 m is therefore
\[ 40 - 28 = 12 \text{ competitors (accept 10 to 14)} \] [1 mark]
A cumulative frequency graph always reads "up to and including" a distance, so finding "more than" a value, as in part (c), requires subtracting the reading from the total.
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