Higher June 2021 Paper 1 Q18

EdexcelHigherCurrent spec5 marksHistograms

18 The table and histogram give information about the distance travelled, in order to get to work, by each person working in a large store.

Distance (d km)	Frequency
\(0 \leqslant d \lt 10\)	40
\(10 \leqslant d \lt 15\)
\(15 \leqslant d \lt 20\)
\(20 \leqslant d \lt 30\)
\(30 \leqslant d \lt 60\)	30

Histogram with Distance travelled (km) from 0 to 60 on the horizontal axis and Frequency density on the vertical axis with no scale; bars are drawn for 0 to 10, 10 to 15, 15 to 20 and 20 to 30 only

Using the information in the table and in the histogram,

(a) complete the table, (2)

(b) complete the histogram. (1)

One of the people working in the store is chosen at random.

(c) Work out an estimate for the probability that the distance travelled by this person, in order to get to work, was greater than 25 km. (2)

Mark scheme (a)

Scheme	Marks
eg height of first bar labelled as FD 4 or one 1 cm by 1 cm square = 5 people or 1 line of 5 small squares = 1 person or one 2cm by 2 cm square = 20 people etc	M1
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: 35, 39, 56	A1
	(2)

Notes

M1: for the use of frequency density – ie that area is proportional to frequency – with either a correct frequency density unambiguously labelled on axis or for an area representing a correct number of people or 2 correct frequencies completed

A1: All 3 correct

Scheme	Marks
Correct bar	B1
	(1)

Mark scheme (c)

Scheme	Marks
0.5 × “56” + 30 (= 58) or 40 + “35” + “39” + “56” + 30 (= 200)	M1ft
Working not required, so correct answer scores full marks (unless from obvious incorrect working) Answer: \(\dfrac{58}{200}\)	A1ft
	(2)
	(5 marks)

Notes

M1ft: follow through their stated value for \(20 \leqslant d \lt 30\) for total greater than 25 or ft their 3 values in the table for total

A1ft: ft dep on a completed table

oe eg \(\dfrac{29}{100}\) or 0.29 or 29%