This topic provides the formulae used by IBM®
SPSS® Data Collection Survey Reporter to calculate the various types of cell contents. The topic is divided
into two subsections. The first provides the formulae used to calculate
the cell contents that are not dependent on a numeric variable and
the second provides the formulae for the summary statistics of numeric
variables.

Notation

The following table shows the notation used in this topic except
where stated otherwise.

Notation

Description

Sum of cell weights for cases in cell (i, j).

Number of rows contributing to the test

Number of columns contributing to the test

The jth column subtotal:

The ith row subtotal:

The grand total:

The following table provides the formulae used by Survey Reporter to calculate the cell contents that are
not dependent on a numeric variable.

Item

Formula

Count

Column Percentage

Row Percentage

Total Percentage

Indice

Expected Count

Residual

Summary Statistics of Numeric Variables

Notation

The following table shows
additional notation used in the remainder of this topic except where
stated otherwise.

Notation

Description

Value of the variable for case i.

Weight for case i

Number of cases

Sum of the weights for the first i cases

Mean for the first i cases

The following table provides the formulae used by Survey Reporter to calculate the cell contents that are
dependent on a numeric variable, with the exception of percentiles,
the formula for which is shown below the table.

Item

Formula

Mean

Sum

Minimum

Maximum

Range

Mode

Value of Xj that has the largest observed frequency.
If there are several modes, the first one encountered in the data
is selected.

Median

The median is the 50th percentile. See Percentile, which is
shown below.

Variance

Standard Deviation

Standard Error

Percentile

Survey Reporter uses one method for computation
of percentiles. Let

where p is the requested percentile
divided by 100, and k1 and k2 satisfy

Then

Let x be the pth percentile; the definition is as follows: