Write down the mode.

Using your graphic display calculator, write down the value of
(i)     the mean;
(ii)    the standard deviation;
(iii)   the median.

Find the interquartile range.

Draw a box and whisker diagram for this data, on graph paper, using a scale of $1{\text{ cm}}$ to represent $5{\text{ cm}}$.

Sam estimated the value of the mean of the measured lengths to be $43{\text{ cm}}$.

Find the percentage error of Sam’s estimated mean.

$47.5{\text{ (cm)}}$     (A1)

(i)     $45.85{\text{ (cm)}}$     (G2)

Note: Accept $45.9$ .

(ii)    $17.1{\text{ }}(17.0888 \ldots )$     (G1)
(iii)   $47.5{\text{ (cm)}}$     (G1)

$62.5 - 32.5 = 30$     (M1)(A1)(G2)

Note: Award (M1) for correct quartiles seen.

(A1) for correct label and scale
(A1)(ft) for correct median
(A1)(ft) for correct quartiles and box
(A1) for endpoints at $17.5$ and $77.5$ joined to box by straight lines     (A1)(A1)(ft)(A1)(ft)(A1)

Notes: The final (A1) is lost if the lines go through the box. Follow through from their parts (b) and (c).

$\varepsilon  = \left| {\frac{{43 - 45.85}}{{45.85}}} \right| \times 100\%$     (M1)

Note: Award (M1) for their correct substitution in $\%$ error formula.

$= 6.22\%$ ($6.21592 \ldots$)     (A1)(ft)(G2)

Notes: Follow through from their answer to part (b)(i). Accept $6.32\%$ with use of $45.9$ .