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Data Analysis, SM-Bank 025

A shop sells children's shoes in sizes from 5 to 9. The sizes of the last 100 shoes sold is shown in the table below.

\begin{array} {|l|c|c|c|c|c|c|}
\hline \textbf{Shoe Size} & 5 & 6 & 7 & 8 & 9  \\
\hline \textbf{Frequency}  & 14 & 21 & 30 & 23 & 12 \\
\hline \end{array}

  1. What is the median shoe size?  (1 mark)

  2. What is the mean shoe size?  Give your answer correct to the nearest whole number.  (2 marks)

  3. What is the range of shoe sizes?  (1 mark)

  4. What is the modal shoe size?  (1 mark)

  5. Briefly explain why the shop owner would be particularly interested in the modal shoe size?  (2 marks)

Show Answers Only
  1. `7`
  2. `6.98`
  3. `4`
  4. `7`
  5. `text(The shop keeper would be primarily interested in profit,)`
    `text(and the most popular shoe size will generate the most profit.)`
    `text(Also for stock purposes it would be an advantage to have the)`
    `text(most popular size in stock.)`
Show Worked Solution

a.    `text(Median) \ = \text(Average of 50th and 51st scores) \ = 7`

b.    `text(Mean)` `=(5 xx 14 + 6 xx 21 + 7 xx 30 + 8 xx 23 + 9 xx 12)/100`  
  `=(70 + 126 + 210 + 184 +108)/100`  
  `=698/100 = 6.98`  

 
c.    `text(Range) \ = \text(highest score) \-\ text(lowest score) \ = 9 \-\ 5 = 4`

d.    `text(Modal shoe size) \ = \text(The shoe size with the highest frequency) \ = 7`

\begin{array} {ll}
\textbf{e.}&\text{The shop keeper would be primarily interested in profit,}\ \\
&\text{and the most popular shoe size will generate the most profit.}\ \\
&\text{Also for stock purposes it would be an advantage to have the}\ \\ 
&\text{most popular size in stock.}\end{array}