June 2024 Paper 2 Q14

OCR MEICurrent spec8 marksData Processing Large Data Set

14 The pre-release material contains medical data for 103 women and 97 men.

The boxplot represents the weights in kg of 101 of the women from the pre-release material.

Boxplot of weight in kg on a scale from 0 to 140: minimum 41.4, lower quartile 57.7, median 69.5, upper quartile 82.05, maximum 132.2

(a) Use your knowledge of the pre-release material to give a reason why the weights of all 103 women were not included in the diagram. [1]

(b) Determine the range of values in which any outliers lie. [3]

(c) Use your knowledge of the pre-release material to explain whether these outliers should be removed from any further analysis of the data. [1]

(d) The median weight of men in the sample was found to be 79.9 kg.
Explain what may be inferred by comparing the median weight of men with the median weight of women. [1]

Further analysis of the weights of both men and women is carried out. The table shows some of the results.

	mean	standard deviation
men	82.69 kg	19.98 kg
women	72.5 kg	19.95 kg

(e) Use the information in the table to make two inferences about the distribution of the weights of men compared with the distribution of the weights of women. [2]

Scheme	Marks	AO
not all the data were available	B1	2.4
	[1]

Mark scheme (b)

Scheme	Marks	AO
\(57.7 - 1.5 \times (82.05 - 57.7)\) or \(82.05 + 1.5 \times (82.05 - 57.7)\) seen	M1	1.1
outliers \(\lt 21.175\) or outliers \(\gt 118.575\)	A1	2.2a
(hence all outliers in interval) (118.575,132.2] (since no outliers in lower tail)	A1	2.2a
	[3]

Notes

A1: given correct to 1 dp or better; both regions needed; allow non-strict inequalities

A1: allow eg between 118.6 and 132.2
allow strict or non-strict inequalities

if M0 allow SCB1 for both regions outliers \(\lt 21.175\) or outliers \(\gt 118.575\) unsupported;
allow SCB2 for all outliers in (118.575,132.2] unsupported

Mark scheme (c)

Scheme	Marks	AO
should not be removed since no reason to eg doubt that it’s genuine data eg suspect it’s been misrecorded eg doubt since from (US) government	B1	2.4
	[1]

Notes

B1: LDS advantage

Mark scheme (d)

Scheme	Marks	AO
a typical man is heavier than a typical woman, [since \(79.9 \gt 69.5\)]	B1	2.2b
	[1]

Notes

B1: allow
eg an average man is heavier than an average woman

do not allow
eg men are heavier than women on average

Mark scheme (e)

Scheme	Marks	AO
mean weight for men is greater than mean weight for women, so distribution for men is located further along the number line than the distribution for women (by about 10 kg) oe	B1	2.4
standard deviations (or variances) are approximately equal, so similar dispersion about the mean / variation in weights for men and women oe	B1	2.2a
	[2]

Notes

B1: allow mean weight for men greater than mean weight for women, so men are heavier than women (by about 10 kg) oe
must refer to mean or average

B1: must refer to standard deviation or variance