Frequency Tables

The **Frequency Tables **commands construct tables of frequency
counts and percentages for discrete or continuous variables. A frequency table is
a tabular representation of data that can be used to summarize a frequency
distribution of a categorical, nominal or ordinal variable. Each row consists
of five values: *value* (the value of input variable for discrete data or the
class interval for continuous data), *count* (for discrete data: the
number of times the value occurs within the data set; for continuous data: the
number of observations that fall into the bin), *cumulative count*, *percent*,
*cumulative percent*.

# How To

Run: Statistics→Basic Statistics→Frequency Tables (discrete data)... or Frequency Tables (continuous data)...

Select one or multiple input variables.

Optionally, select a frequency variable. Frequency variable specifies the number of observations that each row represents. When omitted, each row represents a single observation.

Optionally, select a break (layer) variable. Break (layer) variable distinct values will cause separate tables to be generated.

*Only complete rows are included (values for an input variable
and for the frequency and layer variables, if any, are not missing). *

Use the Plot histogram option to add a histogram for every frequency table.

Continuous data only**:**

Enter the number of class intervals
or leave the number of intervals option (Advanced Options) equal to zero to create a set of
evenly distributed bins between the variable's minimum and maximum values, the
number of bins is defined as ,
and *N* is the total number of observations for a variable (Sturges,
1926). Please note, that the actual number of intervals may differ due to using
*neat bins* (or *”round” intervals*, i.e. intervals with a width
whose last digit in scientific notation is 1, 2 or 5). The number of intervals
is calculated separately for each input variable.

To use an exact
number and location of class intervals (same for all input variables) – specify
** both **the lower bound (Start value)
and the width of each interval (Interval width).
If there is an observation that is less than the start value or greater than
the upper bound, a bin “

*Up to*“ or “

*More than*” is added to the table.

# Results

Report includes tables with frequency counts for each variable (for each level of the break variable, if any).

### Discrete variables

– i^{th}
observation of the input variable.

Count - the number of observations for each unique value of the input variable ().

Cumulative Count - the number of observations with a value less than or equal to the .

Percent – percentage of compared to the count of all observation.

Cumulative Percent - percentage of the observations with a value less than or equal to the compared to the count of all observation.

### Continuous variables

to – interval (bin range).

Count - the number of observations falling within bin range.

Cumulative Count -
the number of observations with the value less than *or equal* to the right
boundary of the bin (for left-closed bins – *strictly less* than the right
boundary of the bin).

Percent – percentage of observations compared to the count of all observation.

Cumulative Percent - percentage of the observations with a value less than or equal to the right boundary of the range compared to the count of all observation.

# Example

The grades awarded for the assignment set for the class of
22 students are as follows:

Example: [Freq Tables dataset, “Grade” variable]

To construct the frequency table: run the Statistics→Basic Statistics→ Frequency Tables (continuous data) command and select the Grade column as the input variable. Then group the data into five class intervals from 1 to 100: set the interval width to 20, set the number of intervals to 5 and set the start value to 0.

The report produced includes the frequency table and the histogram for the Grade variable.

From the third row we can see that 22.7% of students have grades between 40 and 60 and approximately 45% of students were scored less than or equal to 60 (right-closed intervals).

# References

Sturges, H. A. (1926). The choice of a class interval. Journal of the American Statistical Association, 21, 65–66.

Velleman, P. F., & Hoaglin, D. C. (1981). Applications, basics, and computing of exploratory data analysis. Boston, Mass: Duxbury Press.