Hint
Use the explicitly stated median-of-halves convention. Take the mean of the fourth and fifth lower-half values.
Worked solution
(a)
\(\displaystyle \frac{13+ 14}{2}= \frac{27}{2}\)
Answer: \(\displaystyle \frac{27}{2}\).
Answer: \(\displaystyle \frac{27}{2}\)
(b)
\(\displaystyle \frac{22+ 23}{2}= \frac{45}{2}\)
Answer: \(\displaystyle \frac{45}{2}\).
Answer: \(\displaystyle \frac{45}{2}\)
(c)
\(Q_3-Q_1=9\)
Answer: \(9\).
Answer: \(9\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit valid alternative reasoning and consequential working; do not award a reasoning mark for an unexplained final answer.
(a) · 2 marks
- 1 mark: Take the mean of the fourth and fifth lower-half values.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not confuse an outlier fence with an observed extreme.
(b) · 2 marks
- 1 mark: Take the median of the upper eight observations.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Use \(\displaystyle Q_{3}-Q_{1}\), not \(\displaystyle Q_{3}\)−median, for the IQR.
(c) · 2 marks
- 1 mark: Subtract the first quartile from the third.
- 1 mark: Obtain the stated result with the required sign, units and domain.
Alternative methods: Any complete mathematically valid method with the stated assumptions and equivalent result is acceptable.
Common error: Do not confuse an outlier fence with an observed extreme.
Total: 6 marks.