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Date May 2013 Marks available 2 Reference code 13M.1.sl.TZ1.8
Level SL only Paper 1 Time zone TZ1
Command term Determine Question number 8 Adapted from N/A

Question

The weights, in kg, of 60 adolescent females were collected and are summarized in the box and whisker diagram shown below.

Write down the median weight of the females.

[1]
a.

Calculate the range.

[2]
b.

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

[1]
c.

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.

[2]
d.

Markscheme

42 kg     (A1)     (C1)


Note: The units are required.

a.

58 − 33     (A1)


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

= 25     (A1)     (C2)

b.

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

c.

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).

d.

Examiners report

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.

a.

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.

b.

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.

c.

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.

d.

Syllabus sections

Topic 2 - Descriptive statistics » 2.5 » Measures of central tendency.
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