Statistics: Variance, Standard Deviation, and Degrees of Freedom

Vocabulary practice flashcards generated from lecture transcript chapters on statistical variance formulas, sample vs. population metrics, degrees of freedom, and normal distributions.

Computational Formula for Variance

A method for calculating variance using raw sums ($\sum X$ and $\sum X^2$) that avoids the need to subtract the mean from every individual score before squaring.

Definitional Formula for Variance

A formula for variance where each individual score is subtracted from the mean, squared, and summed to determine the sum of squares ($SS$).

Sum of Squares ($SS$)

The total sum of squared deviation scores representing how much individual scores vary around the mean.

Degrees of Freedom ($df$)

Defined as $n - 1$ for a sample, it represents the number of scores in a dataset that are free to vary around the mean while preserving a fixed mean value.

Sample Variability Bias

The statistical property where variability in a sample naturally underestimates the variability of the larger population from which it was drawn.

Sample Variance ($s^2$)

An accurate estimate of population variance calculated from sample data using degrees of freedom ($n - 1$) in the denominator: $s^2 = \frac{SS}{n - 1}$.

Population Variance ($\times$ or $\text{sigma}^2$ / $\text{sigma}$)

The variance of an entire population, calculated using total population size ($N$) in the denominator and population mean ($\text{mu}$): $\text{sigma}^2 = \frac{\text{sum}(X - \text{mu})^2}{N}$.

Effect of Adding a Constant to Every Score

Adding a constant increases the mean by that exact constant value, but leaves the standard deviation and variance unchanged because the relative distances between scores remain identical.

One Standard Deviation Unit (Normal Curve)

The range between $-1$ and $+1$ standard deviation from the mean in a normal distribution, containing 68.26\text{\textpercent} of all scores (34.13\text{\textpercent} on each side of the mean).