A-LevelMathematicsProbability and statistics9709/53 · May/June 2020 · Q610 Marks
The annual salaries, in thousands of dollars, for 11 employees at each of two companies A and B are shown below. Company A 30 32 35 41 41 42 47 49 52 53 64 Company B 26 47 30 52 41 38 35 42 49 31 42
- (a)Represent the data by drawing a back-to-back stem-and-leaf diagram with company A on the left-hand side of the diagram.[4]
- (b)Find the median and the interquartile range of the salaries of the employees in company A.[3]
- (c)A new employee joins company B. The mean salary of the 12 employees is now $38 500. Find the salary of the new employee.[3]
This question uses a diagram from the original paper, which isn't shown here. Open the full paper from the past papers archive to see it.
Mark scheme
Marking points from the official mark scheme (May/June 2020). The mark or mark type is shown in brackets.
- [B1] Correct stem
- [B1] Correct A on LHS
- [B1] Correct B on same diagram
- [B1] Correct key for their diagram, both companies identified and correct units
- [B1] Median = [$]42 000
- [B1] LQ = [$]35 000
- [B1] UQ = [$]52 000
- [B1 FT] IQR = [$]17 000 (FT if 49000 <= UQ <= 53000 - 32000 <= LQ <= 41000)
- [M1] Sum of given 11 numbers is 433 000
- [M1] Sum of 12 numbers, including new = 38 500 × 12 = 462 000
- [A1] Difference = new salary = [$]29 000
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