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.
