Standard Deviation, SM-Bank 006

Seven players in two basketball teams, the Swifties and the Chiefs, recorded how many 3-point baskets they had shot in the last season.

The results are recorded in the two Stem and Leaf plots below.

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

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

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Show Answers Only

i. \(\text{Std Dev}\ = 13.4 \)

ii. \(\text{The results of the Chiefs have a much smaller range (18 vs 38)}\)

\(\text{and are a much tighter fit around the expected mean.}\)

\(\text{The Chiefs’ results will therefore have a smaller standard deviation.}\)

Show Worked Solution

i. \(\text{Swifties’ dataset:}\ 1, 2, 17, 22, 26, 33, 39 \)

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

\(\text{Std Dev}\ = 13.43… = 13.4\ \text{(1 d.p.)} \)

ii. \(\text{The results of the Chiefs have a much smaller range (18 vs 38)}\)

\(\text{and are a much tighter fit around the expected mean.}\)

\(\text{The Chiefs’ results will therefore have a smaller standard deviation.}\)