Hint
Use population variance when describing the complete listed data set. Add all observations and divide by nine.
Worked solution
(a)
\(\bar x=19\)
Answer: \(19\).
Answer: \(19\)
(b)
\(\displaystyle \operatorname{Var}(X)= \sum \frac{x^{2}}{9}- \bar{x}^{2}= \frac{160}{9}\)
Answer: \(\displaystyle \frac{160}{9}\).
Answer: \(\displaystyle \frac{160}{9}\)
(c)
\(x_{(5)}=19\)
Answer: \(19\).
Answer: \(19\)
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: Add all observations and divide by nine.
- 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 divide descriptive population variance by n−1.
(b) · 2 marks
- 1 mark: Calculate the second moment and subtract the square of the mean.
- 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: A change in location does not by itself change spread.
(c) · 2 marks
- 1 mark: Locate the fifth ordered observation.
- 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 divide descriptive population variance by n−1.
Total: 6 marks.