Standard Deviation of Frequency Distribution by Hand (Leaving Cert Mathematics): Flashcards

Spread of data around the mean

$s = \sqrt{\frac{\sum f(x - \bar{x})^2}{\sum f}}$

Midpoint of each class interval

Mean of the distribution

Frequency of each class

Total frequency

$\bar{x} = \frac{\sum (f \times x)}{\sum f}$

Calculate the mean $\bar{x}$

Find deviations $(x - \bar{x})$

Square the deviations $(x - \bar{x})^2$

Multiply squared deviations by frequency $f$

Sum all $f(x - \bar{x})^2$ values

Divide by $\sum f$ and take square root