A box plot from a curve
A box plot from a curve
Secondary 4
7 marks
The cumulative frequency curve shows the lengths of \(60\) fish caught in Pond A. The curve starts at \(10\) cm and ends at \(40\) cm.
- Use the curve to find the five values needed for a box-and-whisker plot. Use the ends of the curve as the smallest and largest lengths.[3]
- Draw the box-and-whisker plot for Pond A on the scale below, above the plot for Pond B.[2]
- Make two comments comparing the lengths of the fish in the two ponds.[2]
Solution:
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Answer:(a) smallest \(10\), \(Q_1=20\), median \(25\), \(Q_3=30\), largest \(40\) (cm) (b) Box plot with these five values (c) Pond B’s fish are longer on average (median \(28\) cm against \(25\) cm); Pond A’s lengths are more consistent (IQR \(10\) cm against \(14\) cm).
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