These univariate statistics help describe the distribution of a variable. They each tell you something different about what the distribution looks like.

Measures of Central Tendency

Tell you the value that the "typical" case in the distribution has for your variable.

Measures of Dispersion

Tell you how much variation you have across cases in the distibution of your variable.

Central Tendency

Mode

Nominal measure

Most frequently occuring value in the distribution

NOT the number of times that value occurs

Median

Ordinal measure

The "middle" of the distribution when all cases are arranged in rank order

The value of the case that lies at the point at which 50% have a lower value and 50% have a higher value.

Mean

Interval/Ratio

The arithmetic mean, or what is typically referred to as the average

Σ x / n

Sum (Σ) of all values in the distribution (x) divided by the number of cases (n)

Denoted as an x with a bar over it (for sample data) or μ (for population data)

Measures of Dispersion

Variation Ratio

Nominal

Simply the proportion of cases that are not in the modal category

1-p[Mode]

1 minus the proportion of all cases in the modal category

Limited utility

Range

Ordinal

Difference between the two extremes of the distribution

Highest value found in the distribution minus the lowest value found in the distribution

Limited utility

Standard Deviation

Interval/Ratio

Roughly the "average" amount of deviation in a distribution

Actually the square root of the average sum of squares.

denoted as s (for sample data) or σ (for population data)

Take the difference (deviation) between the value of each case from the mean and square it

Sum all the squared deviations. This result is called the variation, or sum of squares.

Divide by the number of cases, n. (Use n − 1 for sample data.) This result is called the variance.