Complete the following table for the grades obtained by the students.

Write down the modal grade obtained by the students.

Calculate the median grade obtained by the students.

One student is chosen at random from the group.

Find the probability that this student obtained either grade \(4\) or grade \(5\).

     (A2)     (C2)

Notes: Award (A1) for three correct. Award (A0) for two or fewer correct.

[2 marks]

\({\text{Mode}} = 6\)     (A1)(ft)     (C1)

[1 mark]

\({\text{Median}} = 4.5\)     (M1)(A1)(ft)     (C2)

Note: (M1) for attempt to order raw data (if frequency table not used) or (M1) halfway between 10^th and 11^th result.

[2 marks]

\(\frac{7}{{20}}{\text{ }}(0.35{\text{, }}35\% )\)     (A1)(ft)     (C1)

[1 mark]

Parts (a) and (b) were well done by the vast majority of candidates.

Parts (a) and (b) were well done by the vast majority of candidates.

Part (c) caused problems to many – with (1) the mean of the two grades not being taken (2) the mean being calculated instead of the median.

Part (d) was successfully completed by those candidates who did the question by counting. Those who tried to use the probability laws were not successful.

Much of the question could have been checked by inputting the data into the GDC.