4MA0 Higher January 2014 Paper 4R Q12

EdexcelHigherOld spec7 marksGrouped Data Histograms

12 Loma grows tomatoes in her garden.
The table shows information about the weights, in grams, of some of her tomatoes.

Weight of tomato (\(w\) grams)	Number of tomatoes
\(0 \lt w \leqslant 10\)	2
\(10 \lt w \leqslant 20\)	8
\(20 \lt w \leqslant 30\)	16
\(30 \lt w \leqslant 40\)	10
\(40 \lt w \leqslant 50\)	4

(a) Work out an estimate for the total weight of these tomatoes. (3)

Loma also grows potatoes.
The incomplete histogram shows information about the weights, in grams, of some of her potatoes.

Incomplete histogram of weight of potato from 0 to 500 grams with an unlabelled frequency density axis

There were 10 potatoes with weights between 100 grams and 150 grams.

(b) How many potatoes had weights less than 100 grams? (2)

There were 12 potatoes with weights between 300 grams and 450 grams.

Mark scheme (a)

Scheme	Marks
(2 x 5) + (8 x 15) + (16 x 25) + (10 x 35) + (4 x 45)	M2
1060	A1
	(3)

Notes

M2: freq x all correct midpoint values stated or evaluated {do not have to see intention to add}.

if not M2 then M1 for freq x consistent point in each interval (\(f \times x\) = 860 or 1260 start & end points).
or M1 for 1 error in list of 10, 120, 400, 350, 180
or M1 for 4 correct products stated.

A1: Accept 26.5 if M2 scored.

Scheme	Marks
1 square = 5 (potatoes) or 1 small square = 0.2 (potatoes) or correct fd calculated (10 ÷ 50) (=0.2) or marked on vertical axis with no errors	M1
8	A1
	(2)

Scheme	Marks
(fd=) 12 ÷ (450 – 300) (= 0.08)	M1
correct block	A1
	(2)
	(7 marks)