The lengths, t minutes, of 242 phone calls made by a family over a period of 1 week are summarised in the frequency table below. Length of phone call (t minutes) 0<t≤1 1<t≤2 2<t≤5 5 < t < 10 10 < t ≤ 30 Frequency 14 46 102 a 40

Mark scheme

Marking points from the official mark scheme (May/June 2018). The mark or mark type is shown in brackets.

1. [B1] (i) a = 40
2. [M1] (ii) Numerator: 5 products with at least 3 acceptable mid-points × appropriate frequency FT (i). Denominator: 242 CAO
3. [A1] (ii) CAO (6.3347... rounded to 3 or more SF)
4. [M1] (iii) Attempt at fd [f/(attempt at cw)] or scaled freq
5. [A1FT] (iii) Correct heights seen on diagram with linear vertical scale from (x, 0) FT their a/5 only
6. [B1] (iii) Correct bar widths (1:1:3:5:20) at axis, visually no gaps, with linear horizontal scale from (0, y), first bar starting at (0,0)
7. [B1] (iii) Labels (time, mins, and fd(OE) seen, some may be as a title) and a linear scale with at least 3 values marked on each axis. (Interval notation not acceptable)