Methods and formulas for Descriptive Statistics (Tables)

Select the method or formula of your choice.

Mean

The mean is the sum of all observations divided by the number of (non-missing) observations. Use the following formula to calculate the mean for each cell or margin using the data corresponding to that cell or margin.

Formula

Notation

TermDescription
xdata value for each observation
ncount of number of observations for each cell or margin

Median

The median is the middle value in an ordered data set. Thus, at least half the observations are less than or equal to the median, and at least half the observations are greater than or equal to the median.

If the number of observations in a data set is odd, the median is the value in the middle. If the number of observations in a data set is even, the median is the average of the two middle values.

Use the following method to calculate the median for each cell or margin using the data corresponding to that cell or margin.
N is odd
For example, when N = 5, and you have ordered data (smallest value to largest value), x1, x2, x3, x4, and x5, then the median = x3.
N is even
For example, when N = 6, and you have ordered data (smallest value to largest value), x1, x2, x3, x4, x5, and x6, then:

Minimum

The smallest data value that is in a table cell or margin.

Maximum

The largest data value that is in a table cell or margin.

Sum

The sum is the total of all the data values that are in a table cell or margin.

Sum = Σ x

Standard deviation

The standard deviation is the most common measure of dispersion, or how spread out the data are about the mean. The more widely the values are spread out, the larger the standard deviation. The standard deviation is calculated by taking the square root of the variance.

Formula

Use this formula to calculate the standard deviation for each cell or margin using the data from that cell or margin.

Notation

TermDescription
xdata value for each observation
mean for each cell or margin
ncount of number of observations for each cell or margin

N Nonmissing

The number of non-missing observations that are in a table cell or margin.

N Missing

The number of missing observations that are in a table cell or margin.

Counts

Formula

The count is the number of times each combination of categories occurs.

Row percent

Formula

The row percent is obtained by multiplying the ratio of a cell count to the corresponding row total by 100 and is given by:

Notation

TermDescription
n i+ number of observations in the i th row
nij number of observations in the cell corresponding to i th row and j th column

Column percent

Formula

The column percent is obtained by multiplying the ratio of a cell count to the corresponding column total by 100 and is given by:

Notation

TermDescription
n +j counts of all the observations in the j th column
nij counts of observations in the cell corresponding to i th row and j th column

Total percents

Formula

The total percent is obtained by multiplying the ratio of a cell count to the total number of observations by 100 and is given by:

Notation

TermDescription
n ++ number of observations in the table
nij number of observations in the cell corresponding to i th row and j th column
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