6 An online store has a total of 930 different types of women's running shoe on sale. The prices in pounds of the types of women's running shoe are summarised in the table below.
| Price \(( \pounds x )\) | \(10 \leqslant x \leqslant 40\) | \(40 < x \leqslant 50\) | \(50 < x \leqslant 60\) | \(60 < x \leqslant 80\) | \(80 < x \leqslant 200\) |
| Frequency | 147 | 109 | 182 | 317 | 175 |
- Calculate estimates of the mean and standard deviation of the shoe prices.
- Calculate an estimate of the percentage of types of shoe that cost at least \(\pounds 100\).
- Draw a histogram to illustrate the data.
The corresponding histogram below shows the prices in pounds of the 990 types of men's running shoe on sale at the same online store.
\includegraphics[max width=\textwidth, alt={}, center]{aff0c5b2-011b-49a0-bf05-6d905f890eba-4_643_1192_340_440} - State the type of skewness shown by the histogram for men's running shoes.
- Martin is investigating the percentage of types of shoe on sale at the store that cost more than \(\pounds 100\). He believes that this percentage is greater for men's shoes than for women's shoes. Estimate the percentage for men's shoes and comment on whether you can be certain which percentage is higher.
- You are given that the mean and standard deviation of the prices of men's running shoes are \(\pounds 68.83\) and \(\pounds 42.93\) respectively. Compare the central tendency and variation of the prices of men's and women's running shoes at the store.