From algebraic pie sectors to a histogram

From algebraic pie sectors to a histogram

Secondary 2
TGM Original Questions

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.

    1. Find the total number.
    2. Find the number in \(20<t\le30\).
    1. Complete a frequency table for the five stated intervals.
    2. Draw a histogram with those class boundaries.
    3. Explain why the histogram is a better representation of the grouped continuous times.

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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