Hint
Use the stated units and precision. Average the class boundaries.
Worked solution
(a)
Average the class boundaries.
The mean of its two boundaries is \(\displaystyle \frac{21}{2}\).
Answer: \(\displaystyle \frac{21}{2}\)
(b)
Count every observation once using the disjoint classes.
Adding all three frequencies gives 23.
Answer: \(23\)
(c)
Use each class midpoint times frequency, then divide by total frequency.
The midpoint-weighted total is \(\displaystyle \frac{469}{2}\); divide by 23 to obtain \(\displaystyle \frac{469}{46}\).
Answer: \(\displaystyle \frac{469}{46}\)
Maths4U indicative marking guidance
Maths4U indicative marking guidance, not an official mark scheme. Credit complete valid alternative methods and consequential reasoning. An unexplained result does not earn a method mark.
(a) · 2 marks
- 1 mark: Average the class boundaries.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
(b) · 2 marks
- 1 mark: Count every observation once using the disjoint classes.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Check the answer against the original conditions.
(c) · 2 marks
- 1 mark: Use each class midpoint times frequency, then divide by total frequency.
- 1 mark: Give the correct requested result, retaining signs, units and any domain restrictions.
Alternative methods: Any complete mathematically valid alternative method with the same restrictions and equivalent exact result is acceptable.
Common error: Keep intermediate values exact until the final step.
Total: 6 marks.