Write down the median weight of the females.

Calculate the range.

Estimate the probability that the weight of a randomly chosen female is more than 50 kg.

Use the box and whisker diagram to determine if the mean weight of the females is less than the median weight. Give a reason for your answer.

42 kg     (A1)     (C1)

Note: The units are required.

58 − 33     (A1)

Note: Award (A1) for correct maximum and minimum seen.

= 25     (A1)     (C2)

\(\frac{1}{4}(0.25,25\% )\)     (A1)     (C1)

Mean weight is more than the median weight.     (A1)

The upper half of the distribution is wider (more dispersed) or data is positively (or right) skewed or equivalent reason.     (R1)

OR

\(\left( {{\text{The mean is calculated }}\bar x = \frac{{35.5 \times 15 + 40 \times 15 + 54 \times 15}}{{60}}} \right)\)

\(\bar x = 43.875{\text{ }} (kg)\)     (R1)     (C2)

Note: Do not award (A1)(R0).

Many candidates omitted the “kg” units that were required for the median weight. It is not only area and volume answers where marks may be lost for either missing or incorrect units. Candidates confused IQR with range. Only the very strongest candidates were able to deduce from a box and whisker plot that the data was asymmetric (with a positive skew) hence the mean was greater than the median. This was one of two reasoning marks in the paper and only the very strongest candidates wrote down a correct reason.

Many candidates omitted the “kg” units that were required for the median weight. It is not only area and volume answers where marks may be lost for either missing or incorrect units. Candidates confused IQR with range. Only the very strongest candidates were able to deduce from a box and whisker plot that the data was asymmetric (with a positive skew) hence the mean was greater than the median. This was one of two reasoning marks in the paper and only the very strongest candidates wrote down a correct reason.

Many candidates omitted the “kg” units that were required for the median weight. It is not only area and volume answers where marks may be lost for either missing or incorrect units. Candidates confused IQR with range. Only the very strongest candidates were able to deduce from a box and whisker plot that the data was asymmetric (with a positive skew) hence the mean was greater than the median. This was one of two reasoning marks in the paper and only the very strongest candidates wrote down a correct reason.

Many candidates omitted the “kg” units that were required for the median weight. It is not only area and volume answers where marks may be lost for either missing or incorrect units. Candidates confused IQR with range. Only the very strongest candidates were able to deduce from a box and whisker plot that the data was asymmetric (with a positive skew) hence the mean was greater than the median. This was one of two reasoning marks in the paper and only the very strongest candidates wrote down a correct reason.