Averages (including IQR): Eduqas GCSE Foundation June 2024 Paper 1 Q23

Foundation June 2024 Paper 1 Q23

EduqasFoundationCurrent spec4 marksAverages (including IQR)Grouped Data

23. Pippa and Joe are working on a school project.
The project is based on the use of the local leisure facilities.

(a)

Pippa decides to ask adults how much they spend on gym membership each month.
In the box below, write a suitable question with appropriate response boxes to collect this information. [2]

Question

Response boxes

(b)

Joe asked some adults how many hours they each spent at the leisure centre during the previous week.
His results are shown below.

Number of hours	0–4	5–9	10–14	15–19	20–24
Number of adults	9	2	1	1	2

Joe accurately calculated an estimate of the mean time spent per adult to be 7 hours.

In his project he stated:

‘On average, the adults in my survey each spent 7 hours at the leisure centre last week.’

(i) Explain why the mean is not the best average to use for this data. [1]

(ii) Give one other reason why Joe’s results may not be reliable. [1]

Mark scheme (a)

Scheme	Marks	Comments
An appropriately worded question e.g. How much do you spend each month on gym membership? AND An appropriate set of response boxes e.g. \(c\) = £0, £0 < \(c\) ≤ £10, £10 < \(c\) ≤ £20, \(c\) > £20 less than £10, £10-£20, more than £20	B2	Question must include ‘each month’, There must be a minimum of 3 response boxes which: do not overlap cover all amounts including £0 and no upper limit with the exception of allowing a consistent £1 gap e.g. £0 £1 to £10, £11 to £20, £21 or more Note: If inequalities are used then allow e.g. < 5, 5 - 10, 11 - 15, > 15 OR 5 >, 5 - 10, 11 - 15, 15 < OR 0 ≤ 10, 11 ≤ 20, 21 ≤ 30, ≥ 31 where the inequalities are in the correct directions and the groups are clear. Treat as one error incorrect use e.g. 0 ≥10, 11 ≥ 20, 21 ≥ 30, 31 ≥ B1 for one of the following: an appropriately worded question with no more than ‘one identified error’ from above response boxes. a question that does not include ‘per month’ but with no errors in the response boxes.

Scheme

Marks

Comments

An appropriately worded question

e.g.
How much do you spend each month on gym membership?
AND
An appropriate set of response boxes

e.g.
\(c\) = £0, £0 < \(c\) ≤ £10, £10 < \(c\) ≤ £20, \(c\) > £20

less than £10, £10-£20, more than £20

Question must include ‘each month’,

There must be a minimum of 3 response boxes which:

do not overlap
cover all amounts including £0 and no upper limit with the exception of allowing a consistent £1 gap e.g.
£0 £1 to £10, £11 to £20, £21 or more

Note: If inequalities are used then allow e.g.
< 5, 5 - 10, 11 - 15, > 15
OR 5 >, 5 - 10, 11 - 15, 15 <
OR 0 ≤ 10, 11 ≤ 20, 21 ≤ 30, ≥ 31
where the inequalities are in the correct directions and the groups are clear.

Treat as one error incorrect use e.g.
0 ≥10, 11 ≥ 20, 21 ≥ 30, 31 ≥

B1 for one of the following:

an appropriately worded question with no more than ‘one identified error’ from above response boxes.
a question that does not include ‘per month’ but with no errors in the response boxes.

Mark scheme (b)

Scheme	Marks	Comments
(i) Appropriate explanation e.g. ‘The mean is affected by the few people who spent a long time (in the leisure centre).’ ‘The mean can be significantly affected by outliers or skew’ ‘It would be more accurate to use the mode’ ‘Most people spent less than 7 hours (in the leisure centre).’ ‘The modal time (or median time) is 0 – 4 hours.’	E1	Do not accept: ‘The mean is not the best average.’
(ii) Appropriate reason e.g. ‘Not enough people asked.’ ‘Many responding 0-4 hours probably didn’t go to the leisure centre’	E1	Do not accept: ‘Some people spend longer than 24 hours’ ‘He only asked in one area’ ‘Only collected data for one week’ ‘They may spend different amounts of hours each week’
	(4)