Box Plots: Eduqas GCSE Higher November 2017 Paper 1 Q11

Higher November 2017 Paper 1 Q11

EduqasHigherCurrent spec7 marksBox Plots Cumulative Frequency

11.

(a) Battery life is the length of time for which a battery can be used before it needs to be recharged.

One hundred users of the Litestar A tablet computer each recorded the battery life of their tablet.
The diagram shows the distribution of the battery lives recorded, in hours.

Cumulative frequency graph: battery life (hours) from 7 to 11 on the horizontal axis, cumulative frequency from 0 to 110; points plotted at (8, 0), (8.5, 4), (9, 30), (9.5, 78), (10, 94), (10.5, 100) joined by straight lines

(i) How many of these Litestar A tablet computers had a battery life of more than 9·5 hours? [1]

(ii) Use the diagram to complete the table for these Litestar A tablet computers. [3]

Median	Lower Quartile	Upper Quartile	Inter-quartile Range

(b) This box plot shows the distribution of the battery lives recorded by one hundred users of Litestar B tablet computers.

Grid with battery life (hours) from 7 to 11; a box plot for Litestar B with whiskers from 7.5 to 10.4, box from about 7.8 to 9.3 and median at about 8.9; an empty area labelled Litestar A below it

(i) For the Litestar A tablet computers:

The shortest battery life recorded was 8 hours.
The longest battery life recorded was 10·4 hours.

Using this information and the information from part (a), draw the box plot for the Litestar A tablet computers on the grid above. [2]

(ii) Neena wants to buy one of these tablet computers.
She wants the best battery life possible.

Should Neena buy a Litestar A or Litestar B tablet computer?

Litestar A ☐ Litestar B ☐

Give a reason for your decision. [1]

Mark scheme (a)

Scheme

Marks

Comments

(i)
22

(ii)

M	LQ	UQ	IQR
9.2	8.9	9.4 to 9.5	0.5 to 0.6

B1 for correct median

B1 for correct LQ and UQ

B1 FT for correct IQR;
FT ‘their UQ’ – ‘their LQ’ provided one is correct

Mark scheme (b)

Scheme	Marks	Comments
(i) Correct box plot: Whiskers from 8 to 10.4 Box from 8.9 to (9.4 to 9.5) Median at 9.2	B2	FT their values from (a)(ii) B1 FT for 2 out of 3 correct from whiskers, box, median
(ii) Litestar A and a correct reason. e.g. ‘She should buy tablet A as the median is greater (than tablet B).’ or ‘She should buy tablet A as the median is 0.3 hours more (than tablet B).’ or ‘She should buy tablet A as the shortest battery life is ½ hour greater.’ or ‘Tablet A as the Lower quartile is more than the lower quartile of tablet B.’	E1	FT their values from (a)(ii) or their box plot from (b)(i) Allow ‘Every statistic apart from the highest value is greater for Litestar A than for Litestar B.’
	(7)