4MA0 Higher June 2017 Paper 3 Q4

EdexcelHigherOld spec5 marksGrouped Data

4 The table shows information about the lengths, in cm, of 40 leaves.

Length (\(L\) cm)	Frequency
\(0 \lt L \leqslant 1\)	4
\(1 \lt L \leqslant 2\)	5
\(2 \lt L \leqslant 3\)	11
\(3 \lt L \leqslant 4\)	14
\(4 \lt L \leqslant 5\)	6

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

(b) Work out an estimate for the mean length of the 40 leaves.
Give your answer correct to 1 decimal place. (4)

Scheme	Marks
\(3 \lt L \leqslant 4\)	B1
	(1)

Mark scheme (b)

Scheme	Marks
Eg 0.5×4 + 1.5×5 + 2.5×11 + 3.5×14 + 4.5×6 or 2 + 7.5 + 27.5 + 49 + 27 or 113	M2
(0.5 × 4 + 1.5 × 5 + 2.5 × 11 + 3.5 × 14 + 4.5 × 6) ÷ 40 or 113 ÷ 40	M1
2.8	A1
	(4)
	(5 marks)

Notes

M2: \(f \times d\) for at least 4 products with correct mid-interval values and intention to add.

If not M2 then award M1 for
\(d\) used consistently for at least 4 products within interval (including end points) and intention to add
or
for at least 4 correct products with correct mid-interval values with no intention to add

M1: dep on M1 (ft their products)
NB: accept their 40 if addition of frequencies is shown

A1: Allow 2.82, 2.83 or 2.825