Standard Deviation, SM-Bank 002

Ali’s class sits a Geography test and the results are recorded below.

\(58,\ \ 74,\ \ 65,\ \ 66,\ \ 73,\ \ 71,\ \ 72,\ \ 74,\ \ 62,\ \ 70\)

The mean for the test was 68.5.

Calculate the standard deviation for the test. Give your answer correct to one decimal place. (2 marks)

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Explain whether the mean of the test is greater than or less than the median of the test. (1 mark)

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i. \(5.2\ \ \text{(to 1 d.p.)} \)

ii. \(\text{Median}\ = \dfrac{70+71}{2} = 70.5 \)

\(\Rightarrow\ \text{Median > Mean (70.5 > 68.5)} \)

Show Worked Solution

i. \(\text{By calculator (in Statistics mode):}\)

\(\text{Std Dev}\ = 5.220… = 5.2\ \text{(1 d.p.)} \)

♦ Mean mark (a) 39%.

ii. \(\text{Reorder test results in ascending order:}\)

\(58,\ \ 62,\ \ 65,\ \ 66,\ \ 70, \ \ 71,\ \ 72,\ \ 73,\ \ 74,\ \ 74\)

\(\text{Median}\ = \dfrac{70+71}{2} = 70.5 \)

\(\Rightarrow\ \text{Median > Mean (70.5 > 68.5)} \)