Averages (including IQR): WJEC GCSE Numeracy Higher June 2019 Unit 1 Q6

Numeracy Higher June 2019 Unit 1 Q6

WJECHigherCurrent spec6 marksAverages (including IQR)Box Plots

(a) Maesystrad, Rhewlteg and Glanmawr are three colleges.
Each college recorded the times Year 12 students took to travel to college.
The results are displayed in the box-and-whisker plots below.

Three box-and-whisker plots of travel time in minutes on scales from 0 to 60: Maesystrad min 9, LQ 14, median 34, UQ 45, max 55; Rhewlteg min 9, LQ 14, median 39, UQ 45, max 51; Glanmawr min 9, LQ 14, median 27, UQ 49, max 51

(i) Which of the three colleges has the greatest range of times?
What is the range of times for this college? [1]

College …………………… Range …………………… minutes

(ii) On average, in which college did Year 12 students have the longest travel times?
You must give a reason for your answer. [1]

College: ……………………

Reason: ……………………

(iii) Which college has the greatest difference between the median and the lower quartile?
What is this difference? [1]

College …………………… Difference …………………… minutes

(iv) Which of the three colleges has the greatest number of Year 12 students?
Give a reason for your answer. [1]

Maesystrad ☐ Rhewlteg ☐ Glanmawr ☐ Don’t know ☐

Reason: ……………………

(b) At another college, Wynne College, there are 240 students in Year 12.

The interquartile range of the times taken for these students to travel to college is 32 minutes.

(i) How many of these students have travel times within this interquartile range? [1]

…………………… students

(ii) 75% of the Year 12 students at Wynne College take less than 55 minutes to travel to college.
Complete the following statement.

‘25% of the Year 12 students at Wynne College take less than

…………………… minutes to travel to college.’ [1]

Mark scheme (a)

(i)

Scheme	Marks	Comments
Maesystrad AND 46 (minutes)	B1

(ii)

Scheme	Marks	Comments
Rhewlteg AND gives decision used unambiguously as median	B1	Accept decision based on median without the use of the term ‘median’, e.g. ‘half of them took more than 39 minutes’ Allow, e.g. Rhewlteg as median is 38 (minutes) (from misreading the scale correct median is 39 minutes) Rhewlteg as average is 39 (minutes) Do not accept contradictions, decision needs to be solely based on the median

(iii)

Scheme	Marks	Comments
Rhewlteg AND 25 (minutes)	B1

(iv)

Scheme	Marks	Comments
‘Don’t know’ indicated or unambiguously implied AND reason, e.g. ‘not told’, ‘it doesn’t say (on the diagam)’, ‘doesn’t give you the number of students/pupils’, ‘doesn’t tell you how many were asked’, 'it is about travel times (not number of students)', ‘only gives the timings’, ‘it shows distribution of travel times, not number of students’, ‘only shows proportions of the students’	E1	Allow, e.g. ‘doesn’t give you the frequency (of students)’, Do not accept, e.g. ‘can’t tell’, ‘not enough data’, ‘shows only median, range and measures of spread’