19M.2.AHL.TZ1.H_3

pestleMathematicsAAHLPaper 219M· sl-4-3-mean-median-mode-mean-of-grouped-data-standard-deviation-quartiles-iqrsource ↗

The marks achieved by eight students in a class test are given in the following list.

The teacher increases all the marks by 2. Write down the new value for

Find the mean.

[1]

a.i.

Find the standard deviation.

[1]

a.ii.

the mean.

[1]

b.i.

the standard deviation.

[1]

b.ii.

A ninth student also takes the test.

Explain why the median is unchanged.

[3]

Markscheme / solution

6.75 A1

[1 mark]

a.i.

2.22 A1

[1 mark]

a.ii.

8.75 A1

[1 mark]

b.i.

2.22 A1

[1 mark]

b.ii.

the order is 3, 4, 6, 7, 7, 8, 9, 10

median is currently 7 A1

Note: This can be indicated by a diagram/list, rather than actually stated.

with 9 numbers the middle value (median) will be the 5th value R1

which will correspond to 7 regardless of whether the position of the median moves up or down R1

Note: Accept answers using data 5, 6, 8, 9, 9, 10, 11, 12 (ie from part (b)).

[3 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

b.i.

[N/A]

b.ii.

[N/A]