Paper 4 · statistics - stem and leaf

The masses (g) of 24 sweets, read off a stem-and-leaf diagram and placed in ascending order, are: 0.72, 0.73, 0.79, 0.80, 0.88, 0.91, 0.91, 0.94, 0.98, 0.99, 1.01, 1.03, 1.06, 1.08, 1.13, 1.13, 1.13, 1.19, 1.21, 1.22, 1.33, 1.39, 1.44, 1.45. Find the median mass.

1.03

1.045

1.06

1.07

Explanation: With 24 (an even number of) data values, the median is the mean of the 12th and 13th ordered values: the 12th value is 1.03 and the 13th is 1.06, so the median is

\frac{1.03+1.06}{2}=1.045

g. Taking only the 12th value gives 1.03 g, and taking only the 13th gives 1.06 g; averaging the 13th and 14th values instead of the 12th and 13th gives

\frac{1.06+1.08}{2}=1.07

Derived from ZIMSEC Maths Paper 1, June 2008, Q2 (Statistics)

The masses (g) of 24 sweets, read off a stem-and-leaf diagram and placed in ascending order, are: 0.72, 0.73, 0.79, 0.80, 0.88, 0.91, 0.91, 0.94, 0.98, 0.99, 1.01, 1.03, 1.06, 1.08, 1.13, 1.13, 1.13, 1.19, 1.21, 1.22, 1.33, 1.39, 1.44, 1.45. Find the median mass.

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