Standard Deviation, SM-Bank 014

Albert teaches Physics and sets his class a mid-term exam.

The results are summarised in the Stem and Leaf plot drawn below.

Determine the median test score of the data set. (1 mark)

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Calculate the standard deviation of this data set, giving your answer to two decimal places. (1 mark)

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Show Answers Only

i. \(\text{Median}\ = 83\)

ii. \(\text{Std Dev}\ = 12.14\)

Show Worked Solution

i. \(\text{Dataset values:}\ 62, 65, 78, 79, 83, 89, 94, 96, 97 \)

\(\text{9 data points}\ \ \Rightarrow\ \ \text{Median = 5th value} \)

\(\text{Median}\ = 83\)

ii. \(\text{By calculator (using Statistics mode):} \)

\(\text{Std Dev}\ = 12.139… = 12.14\ \text{(2 d.p.)} \)