Standard Deviation (Sample)

S D = \sqrt{\frac{\sum_{i = 1}^{N} x_{i}^{2}}{N - 1}} = \sqrt{\frac{\sum_{i = 1}^{n} {(X_{i} - \bar{X})}^{2}}{N - 1}}

$SD = sqrt((sum_(i=1)^N x_i^2)/(N-1)) = sqrt((sum_(i=1)^n(X_i-barX)^2)/(N-1))$

(X) Data Set

$(X) "Data Set"$

What does the standard deviation tell us?

A low standard deviation indicates that the data points tend to be close to the mean of the data set, that the data adheres to the central tendency to be close to the mean and not to vary wildly from the mean/

A high standard deviation indicates that the data is spread over a wider range of values.

The Math of the Standard Deviation

The standard deviation of a data set or statistical population is the square root of its variance. The standard deviation, unlike the variance, is expressed in the same units as the data.

The standard deviation ( $σ$ $sigma$ ) expressed as the population SD ( $σ$ $sigma$ ) is:

$σ = \sqrt{\frac{\sum_{i = 1}^{N} (X_{i} - \bar{X})}{N}}$ $sigma = sqrt((sum_(i=1)^N(X_i - barX))/N)$

This means we are calculating the SD on the whole of the data set, the whole population.

Standard Deviation (Sample)

What does the standard deviation tell us?

The Math of the Standard Deviation

See Also