In a school 160 students sat a mathematics examination. Their scores, given as marks out of 90, are summarized on the cumulative frequency diagram.

Write down the median score.

The lower quartile of these scores is 40.

Find the interquartile range.

The lowest score was 6 marks and the highest score was 90 marks.

Draw a box-and-whisker diagram on the grid below to represent the students’ examination scores.

48        (A1) (C1)

\(58 - 40\)        (M1)

Note: Award (M1) for 58 and 40 seen.

\( = 18\)         (A1) (C2)

(A1)(A1)(ft)(A1)(ft)       (C3)

Note: Award (A1) for the correct maximum and minimum, (A1)(ft) for their correct median and (A1)(ft) for 40 and their upper quartile.

Follow through from parts (a) and (b).

Award a maximum of (A1)(A1)(ft)(A0) if the horizontal line goes through the box or if a ruler has clearly not been used.

Question 3: Statistics – boxplot
Whilst there were many fine attempts, the number of poor responses to this question was surprising. The interquartile range was little understood, yet quartiles were correctly plotted. The lack of precision – due mainly to not using a ruler – in drawing the boxplot was also disappointing.

Question 3: Statistics – boxplot
Whilst there were many fine attempts, the number of poor responses to this question was surprising. The interquartile range was little understood, yet quartiles were correctly plotted. The lack of precision – due mainly to not using a ruler – in drawing the boxplot was also disappointing.

Question 3: Statistics – boxplot
Whilst there were many fine attempts, the number of poor responses to this question was surprising. The interquartile range was little understood, yet quartiles were correctly plotted. The lack of precision – due mainly to not using a ruler – in drawing the boxplot was also disappointing.