21M.1.SL.TZ2.5

pestleMathematicsAISLPaper 121M· sl-4-2-histograms-cf-graphs-box-plotssource ↗

The number of sick days taken by each employee in a company during a year was recorded. The data was organized in a box and whisker diagram as shown below:

For this data, write down

the minimum number of sick days taken during the year.

[1]

a.i.

the lower quartile.

[1]

a.ii.

the median.

[1]

a.iii.

Paul claims that this box and whisker diagram can be used to infer that the percentage of employees who took fewer than six sick days is smaller than the percentage of employees who took more than eleven sick days.

State whether Paul is correct. Justify your answer.

[2]

Markscheme / solution

$2$ A1

[1 mark]

a.i.

$6$ A1

[1 mark]

a.ii.

$8$ A1

[1 mark]

a.iii.

EITHER

Each of these percentages represent approximately $25 %$ of the employees. R1

The diagram is not explicit enough to show what is happening at the quartiles regarding $6$ and $11$ / we do not have the data points R1

OR

Discrete data not clear how to interpret “fewer”. R1

THEN

Hence, Paul is not correct (OR no such inference can be made). A1

Note: Do not award R0A1.

[2 marks]

Examiners’ report

[N/A]

a.i.

[N/A]

a.ii.

[N/A]

a.iii.

[N/A]