Data Analysis, SM-Bank 036

The ages of boys competing in an inter-school futsal competition are shown in the frequency distribution table below.

\begin{array} {|c|c|}
\hline \textbf{Age (years)} & \textbf{Frequency} \\
\hline 13 & 4 \\
\hline 14 & 6 \\
\hline 15 & 11\\
\hline 16 & 6\\
\hline 17 & 3\\
\hline \end{array}

How many boys took part in the competition? (1 mark)

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Calculate the mean age of the competitors, correct to the nearest whole number. (2 marks)

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State the median age of the competitors? (2 marks)

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Show Answers Only

\begin{array} {ll} \textbf{a.} & 30 \\ \textbf{b.} & 15 \text{ years} \\ \textbf{c.} & 15 \text{ years} \end{array}

Show Worked Solution

a.	`text( Number of boys)`	`= 4 + 6 + 11 + 6 + 3`
		`= 30`

b.	`text( Mean age of boys)`	`= (13 xx 4 + 14 xx 6 + 15 xx 11 + 16 xx 6 + 17 xx 3)/30`
		`= (52 + 84 + 165 + 96 + 51)/30`
		`= 448/30`
		`= 14.9333…..`
		`~~ 15\ text(years (nearest whole number))`

c.	`text( Median age of boys )`	`= text(average of 15th and 16th scores)`
		`= 15\ text(years, as both the 15th and 16th scores occur in 15 years)`