Hint
Classes are disjoint and their boundaries are explicit. Divide the middle frequency by its class width.
Worked solution
(a)
\(f/w=23/4=\frac{23}{4}\)
Answer: \(\frac{23}{4}\).
Answer: \(\frac{23}{4}\)
(b)
\(\bar t\approx\sum fm/\sum f=\frac{134}{23}\)
Answer: \(\frac{134}{23}\).
Answer: \(\frac{134}{23}\)
(c)
\(\sum fm^2/\sum f-\bar t^2=\frac{5458}{529}\)
Answer: \(\frac{5458}{529}\).
Answer: \(\frac{5458}{529}\)
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: Divide the middle frequency by its class width.
- 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 frequency density rather than frequency for unequal-width bars.
(b) · 2 marks
- 1 mark: Weight each class midpoint by its frequency.
- 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 average the midpoints without frequency weights.
(c) · 2 marks
- 1 mark: Use the weighted midpoint second moment.
- 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 frequency density rather than frequency for unequal-width bars.
Total: 6 marks.