Averages (including IQR): WJEC GCSE Numeracy Intermediate June 2017 Unit 2 Q15

Numeracy Intermediate June 2017 Unit 2 Q15

15. Simon plans to make gloves.

(a)

One morning, Simon decided to carry out a survey to find the mean hand span of people in Wales.

He decided to sample systematically.
He decided to sample from the first 240 people who pass him in the street during the morning.

He wanted to take 20 people’s hand span measurements.
Explain how Simon could use systematic sampling to obtain 20 measurements. [1]

(b)

Yesterday morning, Simon only managed to sample 10 people.
He calculated the mean hand span of these 10 people to be 22·8 cm.

Yesterday afternoon, Simon recorded the hand spans of a further 20 people.

The results for these 20 people are shown in the frequency table below.

Calculate an estimate of the mean of all 30 hand spans that Simon measured yesterday. [6]

(c)

What could Simon do to improve his estimate of the mean hand span of people in Wales? [1]

Mark scheme (a)

Scheme	Marks	Comments
Method of systematic sampling, e.g. ‘(select one person from the first 12 people at random then) ask every (240÷20 =) 12th person’	E1	Note to markers: There should really be mention of the first person being selected at random, however in this first assessment, with only 1 mark available, not doing so will be condoned in this mark scheme

Mark scheme (b)

Scheme	Marks	Comments
Mid points 20.4, 21.3, 22.2, 23.1	B1
20.4×2 + 21.3×3 + 22.2×10 + 23.1×5 (= 40.8 + 63.9 + 222 + 115.5 = )	M1	FT ‘their mid points’ provided they are all within or at the bounds of the appropriate groups
(Sum of 20 hand spans is) 442(.2 cm)	A1	OR estimate of the mean (442.2÷20 =) 22(.11 cm) May be implied in further working
(Sum of all 30 hand spans is) 10×22.8 + 442(.2) (= 670(.2) cm)	M1	OR 10×22.8 + 20×22(.11) FT ‘their derived 442.2’ provided the correct method seen, including where one of ‘their mid points’ was outside the group
÷30	m1	Intention to divide the sum of 30 measurements by 30
22(.34 cm)	A1	Depends on M1, M1 and m1 previously awarded (Watch for an answer 22(.. cm) from \(\dfrac{22.1(1) + 22.8}{2}\) , award B1M1A1M0m0A0)

Mark scheme (c)

Scheme	Marks	Comments
Improvement suggestion, e.g. ‘ask more people’, ‘take a bigger sample’, ‘ask every 5^th person instead’, 'collect more data (from different regions in Wales)', 'use all the raw data', ‘do both hands’, ‘stratified sample on age’, ‘stratified sample on gender’, ‘by narrowing the groups in the table’	E1	Allow, e.g. ‘ask people of different ages’ Do not accept, e.g. ‘measure more accurately’