# Descriptive statistics

A graph of a normal bell curve showing statistics used in standardized testing assessment. The scales include standard deviations, cumulative percentages, percentile equivalents, Z-scores, T-scores, standard nines, and percentages in standard nines.

## Measurements of central tendency

• Mean In general understanding, the mean is the average. Suppose there are five people. The people have, respectively, 1 TV in their house, 4 TVs, 2 TVs, no TVs and 3 TVs. You would say that the 'mean' number of TVs in the house is 2 (1+4+2+0+3)/5=2.
• Median The median is the point at which half are above and half are below. In the above example, the median is also 2, because in this group of 5 people, 2 people have more than 2 TVs in their house and 2 people have fewer than 2 TVs in their house.

## Measurements of variation

• Standard deviation (SD) is a measure of variation or scatter. The standard deviation does not change with sample size.
• Variance is the square of the standard deviation:
$s^2$
• Standard error of the mean (SEM) measures the how accurately you know the mean of a population and is always smaller than the SD.[1] The SEM becomes smaller as the sample size increases. The sample standard devision (S) and SEM are related by:
$SE_\bar{x}\ = \frac{s}{\sqrt{n}}$