Standard Deviation, SM-Bank 009

Isa Guha recorded the number of sixes hit in the first nine games of the Women's Big Bash Cricket League over two seasons.

The results are recorded in the two dot plots below.

Determine the standard deviation of the results in Season 1, giving your answer correct to one decimal place. (2 marks)

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Without using calculations, explain which data set will have the highest standard deviation. (2 marks)

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Show Answers Only

i. \(\text{Std Dev}\ = 1.9\ \text{(1 d.p.)} \)

ii. \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\)

Show Worked Solution

i. \(\text{Season 1 dataset:}\ 6, 6, 7, 8, 10, 10, 10, 11, 11\)

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

\(\text{Std Dev}\ = 1.930… = 1.9\ \text{(1 d.p.)} \)

ii. \(\text{By inspection, season 1 has a slightly higher range}\)

\(\text{(5 vs 4) and its data points can be seen to be much}\)

\(\text{wider spread about the expected mean value.}\)

\(\text{Season 1 will therefore have a higher standard deviation.}\)