18M.1.SL.TZ1.T_6

pestleMathematicsAASLPaper 118M· sl-4-2-histograms-cf-graphs-box-plotssource ↗

In a high school, 160 students completed a questionnaire which asked for the number of people they are following on a social media website. The results were recorded in the following box-and-whisker diagram.

The following incomplete table shows the distribution of the responses from these 160 students.

Write down the median.

[1]

Complete the table.

[2]

Write down the mid-interval value for the 100 < x ≤ 150 group.

[1]

c.i.

Using the table, calculate an estimate for the mean number of people being followed on the social media website by these 160 students.

[2]

c.ii.

Markscheme / solution

* This question is from an exam for a previous syllabus, and may contain minor differences in marking or structure.

180 (A1) (C1)
[1 mark]

36, 24 (A1)(A1) (C2)

Note: Award (A0)(A1) for two incorrect values that add up to 60.

[2 marks]

125 (accept 125.5) (A1)

c.i.

$\frac{{4 \times 25 + 36 \times 75 + 34 \times 125 + 46 \times 175 + 24 \times 225 + 16 \times 275}}{{160}}$ (M1)

Note: Award (M1) for correct substitution of their mid-interval values, multiplied by their frequencies, into mean formula.

=156 (155.625) (A1)(ft) (C3)

Note: Follow through from parts (b) and (c)(i).

[3 marks]

c.ii.

Examiners’ report

[N/A]

c.i.

[N/A]

c.ii.