80 people were each asked how much they spent on clothes last month. The results are summarised in the table below. Amount spent ($ c) Frequency 0 < c ≤ 20 3 20 < c ≤ 40 8 40 < c ≤ 60 14 60 < c ≤ 80 21 80 < c ≤ 100 18 100 < c ≤ 120 9 120 < c ≤ 140 5 140 < c ≤ 160 2 [Figure: Graph grid provided for plotting on the opposite page]

1. (a)Calculate an estimate of the mean amount spent on clothes last month.[3]
2. (b)Complete the cumulative frequency table below. Amount spent ($ c) c ≤ 20 c ≤ 40 c ≤ 60 c ≤ 80 c ≤ 100 c ≤ 120 c ≤ 140 c ≤ 160 Cumulative frequency 3 11 80[1]
3. (c)On the grid opposite, draw a cumulative frequency curve to represent this data.[2]
4. (d)(i)Use your graph to estimate the median.[1]
5. (d)(ii)Use your graph to estimate the interquartile range.[2]
6. (e)The number of people who spent more than $85 last month is the same as the number of people who spent between $k and $85. Given that k is less than 85, use your graph to estimate the value of k.[3]

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