Hint

Use the n/4, n/2 and 3n/4 positions for the specified grouped-data interpolation. Interpolate the n/2 position in the middle class.

Worked solution

(a)

\(Q_2=12+24\frac{76-38}{76}=24\)

Answer: \(24\).

Answer: \(24\)

(b)

\(Q_3-Q_1=36-12=24\)

Answer: \(24\).

Answer: \(24\)

(c)

The cumulative increase over that class is 76.

Answer: \(76\).

Answer: \(76\)

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: Interpolate the n/2 position in the middle class.
• 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: Class frequencies are differences of cumulative totals.

(b) · 2 marks

• 1 mark: Read both quartile positions before subtracting.
• 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 interpolate with the cumulative count as the class frequency.

(c) · 2 marks

• 1 mark: Subtract consecutive cumulative frequencies.
• 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: Class frequencies are differences of cumulative totals.

Total: 6 marks.