Standard Deviation, SM-Bank 015

Rhonda and her friends were surveyed about the number of concerts they have been to in the last 12 months.

Their responses are as follows:

\(3, \ 4, \ 8, \ 10, \ 12, \ 13\)

Determine the median number of concerts from this data set. (1 mark)

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

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Show Answers Only

i. \(\text{Median}\ = 9\)

ii. \(\text{Std Dev}\ = 3.8\)

Show Worked Solution

i. \(3, \ 4, \ 8, \ 10, \ 12, \ 13\)

\(\text{6 data points}\)

\(\text{Median}\ = \dfrac{\text{3rd + 4th}}{2} = \dfrac{8+10}{2} = 9 \)

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

\(\text{Std Dev}\ = 3.771… = 3.8\ \text{(1 d.p.)} \)