4MA0 Higher January 2018 Paper 4R Q6

EdexcelHigherOld spec7 marksAverages (including IQR)Basic Probability

6 The table gives information about the number of goals scored in each of 40 European Championship football matches.

Number of goals scored	Frequency
0	1
1	8
2	12
3	15
4	4

(a) Find the mean number of goals scored. (3)

(b) Work out the interquartile range of the number of goals scored. (2)

Francois has a recording of each of the 40 matches.
He is going to choose at random one of these matches to watch.

Mark scheme (a)

Scheme	Marks
0 × 1, 1 × 8, 2 × 12, 3 × 15, 4 × 4 or 0, 8, 24, 45, 16, 93	M1
\(\dfrac{1 \times 8 + 2 \times 12 + 3 \times 15 + 4 \times 4}{40}\) or \(\dfrac{\text{“}93\text{”}}{40}\)	M1
2.325	A1
	(3)

Notes

M1: For at least 4 products (may not be evaluated.

M1: (dep) for division by 40
NB. If division is by something other than 40 this must clearly come from adding the frequencies.

A1: Accept 2.33 or 2 if 2.325 or \(\dfrac{93}{40}\) seen

Accept \(2\dfrac{13}{40}\)

SCB2 for 2.35

Mark scheme (b)

Scheme	Marks
	M1
1	A1
	(2)

Notes

M1: For Lower Quartile (Q1) = 2 AND Upper Quartile (Q3) = 3
Accept a correct ordered list of the 40 numbers with both quartiles clearly identified in the correct position.

Scheme	Marks
\(\dfrac{15}{40} + \dfrac{4}{40}\) oe	M1
\(\dfrac{19}{40}\)	A1
	(2)
	(7 marks)