Standard Deviation, SM-Bank 012

Seven 40-year old males are asked how many children they have in a survey.

The results are summarised in the histogram drawn below.

Determine the mean number of children of the group surveyed, giving your answer to two decimal places. (1 mark)

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

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Show Answers Only

i. \(\text{Mean}\ = 2.57\)

ii. \(\text{Std Dev}\ = 1.05\)

Show Worked Solution

i. \(\text{Dataset values:}\ 1, 2, 2, 2, 3, 4, 4 \)

\(\text{Mean}\ = \dfrac{1+2+2+2+3+4+4}{7} = \dfrac{18}{7} = 2.571… = 2.57\ \text{(2 d.p.)} \)

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

\(\text{Std Dev}\ = 1.049… = 1.05\ \text{(2 d.p.)} \)