From algebraic pie sectors to a histogram
From algebraic pie sectors to a histogram
Secondary 2
8 marks
TGM Original Questions
Core stretch
Completion times are grouped, in order around the pie chart, into \(0<t\le10\), \(10<t\le20\), \(20<t\le30\), \(30<t\le40\), \(40<t\le50\) minutes. Their sector angles in that same order are \(2x^\circ,x^\circ,(x-12)^\circ,144^\circ,(x+8)^\circ\). The \(144^\circ\) sector represents 36 participants.
- Find the total number.[1]
- Find the number in \(20<t\le30\).[1]
- Construct a frequency table for the five stated intervals.[1]
- Draw a histogram with those class boundaries.[3]
- Explain why the histogram is a better representation of the grouped continuous times.[2]
Solution:
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Answer:(a)(i) \(90\) (ii) \(8\) (b)(i) interval frequencies \(22,11,8,36,13\) (ii) bars on 0–10, 10–20, 20–30, 30–40, 40–50 at those heights (iii) it preserves ordered adjacent intervals and distribution shape.
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