17N.1.SL.TZ0.T_1

pestleMathematicsAASLPaper 117N· sl-4-2-histograms-cf-graphs-box-plotssource ↗

A group of 20 students travelled to a gymnastics tournament together. Their ages, in years, are given in the following table.

N17/5/MATSD/SP1/ENG/TZ0/01

The lower quartile of the ages is 16 and the upper quartile is 18.5.

For the students in this group find the mean age;

[2]

a.i.

For the students in this group write down the median age.

[1]

a.ii.

Draw a box-and-whisker diagram, for these students’ ages, on the following grid.

N17/5/MATSD/SP1/ENG/TZ0/01.b

[3]

Markscheme / solution

$\frac{{14 + 2 \times 15 + 7 \times 16 + 17 + 4 \times 18 + 19 + 20 + 3 \times 22}}{{20}}$ (M1)

Note: Award (M1) for correct substitutions into mean formula.

$( = ){\text{ }}17.5$ (A1) (C2)

[2 marks]

a.i.

16.5 (A1) (C1)

[1 mark]

a.ii.

N17/5/MATSD/SP1/ENG/TZ0/01.b/M (A1)(A1)(A1)(ft) (C3)

Note: Award (A1) for correct endpoints, (A1) for correct quartiles, (A1)(ft) for their median. Follow through from part (a)(ii), but only if median is between 16 and 18.5. If a horizontal line goes through the box, award at most (A1)(A1)(A0). Award at most (A0)(A1)(A1) if a ruler has not been used.

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]