Standard Deviation, SM-Bank 005

9 students completed two quizzes and the results were summarised in the dot plot diagrams below.

Determine the median value of the results of Quiz A. (1 mark)

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Calculate the standard deviation of Quiz A and Quiz B, giving your answers correct to one decimal place. (2 marks)

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Show Answers Only

i. \(\text{Median}\ = 7\)

ii. \(\text{Std Dev (Quiz A)}\ = 1.3 \)

\(\text{Std Dev (Quiz B)}\ = 0.8\)

Show Worked Solution

i. \(\text{9 data points}\ \ \Rightarrow \ \ \text{Median = 5th data point}\)

\(\text{Median}\ = 7 \)

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

\(\text{Quiz A dataset:}\ 5, 5, 6, 7, 7, 8, 8, 8, 9 \)

\(\text{Std Dev (Quiz A)}\ = 1.33… = 1.3\ \text{(1 d.p.)} \)

\(\text{Quiz B dataset:}\ 6, 6, 7, 7, 7, 8, 8, 8, 8 \)

\(\text{Std Dev (Quiz B)}\ = 0.78… = 0.8\ \text{(1 d.p.)} \)