Standard Deviation, SM-Bank 004

Two data sets are represented in the dot plot diagrams below.

Calculate the standard deviation of Data Set B, giving your answer correct to one decimal place. (1 mark)

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

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Show Answers Only

i. \(\text{Std Dev}\ = 1.79… = 1.8\ \text{(1 d.p.)} \)

ii. \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

\(\text{Data Set B will therefore have a higher standard deviation.}\)

Show Worked Solution

i. \(\text{Data points:}\ 4, 4, 5, 5, 6, 6, 7, 8, 9, 9\)

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

\(\text{Std Dev}\ = 1.79... = 1.8\ \text{(1 d.p.)} \)

ii. \(\text{By inspection, Data Set A has a smaller range and a tighter}\)

\(\text{spread against its expected mean value.}\)

\(\text{Data Set B will therefore have a higher standard deviation.}\)