O-LevelMathematicsStatistics4024/22 · May/June 2023 · Q79 Marks

(a) On Monday, the amount of money spent on a website by each customer was recorded. The table shows the results. Amount of money (m) | 0<m≤30 | 30<m≤40 | 40<m≤50 | 50<m≤60 | 60<m≤90 Frequency | p | 18 | 24 | 19 | 24 The histogram shows some of the results. [Figure 7.1] (b) The table shows the amount of money spent on a website by each customer on Tuesday. Amount of money (m) | 0<m≤30 | 30<m≤40 | 40<m≤50 | 50<m≤60 | 60<m≤90 Frequency | 22 | 16 | 24 | 19 | 14

(a)(i)Find the value of p.[1]
(a)(ii)Complete the histogram.[3]
(a)(iii)One of these customers is selected at random to receive a discount voucher. Calculate the probability that this customer spent more than $50 on Monday.[1]
(b)(i)Calculate an estimate of the mean.[3]
(b)(ii)An error was made and one of the sales on Tuesday was not included in the table. That customer spent $41. Tristan says: If that value had been included in the table, then the estimated mean would have been higher. Without calculation, explain why he is correct.[1]

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Mark scheme

Marking points from the official mark scheme (May/June 2023). The mark or mark type is shown in brackets.

[1] 15
[3] B1 for each bar
Completed histogram
After 0 scored, SC1 for 2.4, 1.9 and 0.8 soi
[1] FT 43/(85 + their(a)(i)) provided their (a)(i) is a positive integer
43/100 or 0.43 or 43%
[3] B1 for correct midpoints soi
M1 for (22×15+16×35+24×45+19×55+14×75) / (22+16+24+19+14)
42.8[0] or 42.78 to 42.79
[1] 41 is in 40 < m < 50 so mid-value of 45 would have been used to estimate the mean which is higher than the estimated mean oe

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