Grouped Data: Eduqas GCSE Higher June 2024 Paper 2 Q1

Higher June 2024 Paper 2 Q1

EduqasHigherCurrent spec5 marksGrouped Data

1. 45 students took part in a 400 m race.
Their times, in seconds, were recorded.
The frequency diagram below shows the results.

The groups used are as follows:

\(70 \leqslant \text{time} \lt 80\), \(80 \leqslant \text{time} \lt 90\), \(90 \leqslant \text{time} \lt 100\), \(100 \leqslant \text{time} \lt 110\) and \(110 \leqslant \text{time} \lt 120\).

Frequency diagram of time in seconds: 70 to 80 frequency 5, 80 to 90 frequency 7, 90 to 100 frequency 12, 100 to 110 frequency 11, 110 to 120 frequency 10

Calculate an estimate for the mean time it took to complete the race. [5]

Mark scheme

Scheme	Marks	Comments
Mid-points: 75, 85, 95, 105, 115	B1	May be implied from correct totals, see below.
\(75\times5 + 85\times7 + 95\times12 + 105\times11 + 115\times10\)	M2	FT ‘their mid-points’ provided at least 4 of these are at the bounds or within the groups 375 + 595 + 1140 + 1155 + 1150 (= 4415) M1 for the addition of five products allowing one error with the frequencies. If mid-points are not given, then no marks except for the following cases: B1 M0 for five correct products not added B1 M2 for five correct products in an addition B0 M1 for four correct products in an addition
\(\div\, 45\)	m1
\(98\frac{1}{9}\) or \(\frac{883}{9}\) or 98.1(1…) (seconds)	A1	FT provided M2 m1 awarded, for the correct evaluation using their mid-points Allow 98 from correct working. Allow truncated or rounded decimal FT answers.
	(5)