4MA0 Higher June 2014 Paper 3R Q4

EdexcelHigherOld spec7 marksBasic Probability Grouped Data

4 Freya keeps hens.
The table shows information about the number of boxes of eggs she sold in each of 52 weeks.

Number of boxes sold in a week	Number of weeks
0 to 4	2
5 to 9	6
10 to 14	20
15 to 19	13
20 to 24	8
25 to 29	3

(a) Write down the modal class. (1)

(b) Work out an estimate for the mean number of boxes of eggs that Freya sold each week.
Give your answer correct to 3 significant figures. (4)

Dan picks at random one of the 52 weeks.

Scheme	Marks
10 to 14	B1
	(1)

Mark scheme (b)

Scheme	Marks
\(2 \times 2 + 6 \times 7 + 20 \times 12 + 13 \times 17 + 8 \times 22 + 3 \times 27\) or 4 + 42 + 240 + 221 + 176 + 81 or 764	M2
“764” ÷ 52	M1
14.7	A1
	(4)

Notes

M2: Freq x all correct midpoint values stated or evaluated with intention to add (condone any one error). If not M2 then award M1 for all products \(t \times f\) (and \(t\) is consistently within the interval, including end values) and intention to add (condone any one error)

M1: (dep on at least M1) for division by 52. Accept their 52 if addition shown.

A1: for answer rounding to 14.7
Accept 15 with working (15 without working gains M0A0)

Mark scheme (c)

Scheme	Marks
\(\dfrac{13 + 8 + 3}{52}\)	M1
\(\dfrac{24}{52}\) Answer: \(\dfrac{6}{13}\) oe	A1
	(2)
	(7 marks)

Notes

M1: for 13 + 8 + 3 or 24 or \(\dfrac{a}{52}\) where \(a < 52\)

A1: Accept a decimal/percentage answer 0.461538…(46.15…%) truncated or rounded to 3 or more sig figs. Only accept 0.46 (46%) if preceded by a more accurate answer or M1 (above) awarded.