The times taken, in minutes, to complete a word processing task by 250 employees at a particular company are summarised in the table. Time taken (t minutes) 0 ≤ t < 20 | 20 ≤ t < 40 | 40 ≤ t < 50 | 50 ≤ t < 60 | 60 ≤ t < 100 Frequency 32 | 46 | 96 | 52 | 24

Mark scheme

Marking points from the official mark scheme (Oct/Nov 2022). The mark or mark type is shown in brackets.

1. [M1] At least 4 frequency densities calculated (eg. fd = 32/20) (condone f/cw±0.5 if unsimplified), accept unsimplified, may be read from graph using their scale no lower than 1 cm = fd 1
2. [A1] All bar heights correct on graph, using their suitable linear scale with at least 3 values indicated, no lower than 1 cm = fd 2.
3. [B1] Bar ends at [0,] 20, 40, 50, 60, 100 (at axis), 5 bars drawn 0 < time axis < 100, linear scale with at least 3 values indicated.
4. [B1] Axes labelled frequency density (fd), time (t) and minutes (mins, m) or appropriate title. (Axes may be reversed).
5. [B1] Midpoints 10 30 45 55 80 At least 4 correct midpoints seen (check data table).
6. [M1] Appropriate variance formula with their 5 midpoints (not upper bound, lower bound, class width, frequency density, frequency or cumulative frequency). Condone 1 frequency error. If correct midpoints seen accept [32×10² + 46×30² + 96×45² + 52×55² + 24×80² / 250 - {43.2² or 1866.24} ].
7. [A1] www, final answer 18.25814887 to at least 3SF. If M0 earned SC B1 for final answer 18.25814887 to at least 3SF.