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 \(45.9\) .