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Dataset 1 has mean \(\bar x_1\) and standard deviation \(\sigma_1\).
Dataset 2 has mean \(\bar x_2\) and standard deviation \(\sigma_2\).
Consider the following statement: If \(\bar x_1 < \bar x_2\), then \(\sigma_1 < \sigma_2\).
Is this statement correct? Explain your answer. (2 marks)
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\(\text{Standard deviation is a measure of how much members}\)
\(\text{of a data group differ from the mean value of the group.}\)
\(\text{It follows that the relative standard deviation between two}\)
\(\text{datasets is not affected if}\ \ \bar x_1 < \bar x_2\).
\(\text{Therefore, the statement is incorrect.}\)
\(\text{Standard deviation is a measure of how much members}\)
\(\text{of a data group differ from the mean value of the group.}\)
\(\text{It follows that the relative standard deviation between two}\)
\(\text{datasets is not affected if}\ \ \bar x_1 < \bar x_2\).
\(\text{Therefore, the statement is incorrect.}\)