Standard Deviation (Leaving Cert Mathematics): Quizzes

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Standard Deviation of Frequency Distribution by Hand
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What does the standard deviation measure in a frequency distribution?

The spread of data around the mean

In the formula s=∑f(x−xˉ)2∑fs = \sqrt{\frac{\sum f(x - \bar{x})^2}{\sum f}}, what does xx represent?

Midpoint of each class interval

What does xˉ\bar{x} represent in the standard deviation formula?

Mean of the distribution

Which formula is used to calculate the mean (xˉ\bar{x}) in a frequency distribution?

∑(f×x)∑f\frac{\sum (f \times x)}{\sum f}

What is the first step in calculating standard deviation for grouped data?

Calculate the mean (xˉ\bar{x})

After finding deviations (x−xˉx - \bar{x}), what is the next step?

Square the deviations

In the worked example, what is the mean (xˉ\bar{x}) of the distribution?

31.5

In the worked example, what is the value of ∑f(x−xˉ)2\sum f(x - \bar{x})^2?

1855.00

What is the standard deviation in the worked example?

Approximately 9.63

What is the final operation when calculating standard deviation?

Take the square root

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