# Social Statistics for a Diverse Society

# Chapter Summary

**Chapter 2**

The most basic method for organizing data is to classify the observations into a frequency distribution—a table that reports the number of observations that fall into each category of the variable being analyzed.

Constructing a frequency distribution is usually the first step in the statistical analysis of data.

To obtain a frequency distribution for nominal and ordinal variables, count and report the number of cases that fall into each category of the variable along with the total number of cases (*N*).

To construct a frequency distribution for interval-ratio variables that have a wide range of values, first combine the scores into smaller number of groups—known as class intervals—each containing a number of scores.

Proportions and percentages are relative frequencies. To construct a proportion, divide the frequency (f) in each category by the total number of cases (N).To obtain a percentage, divide the frequency (f) in each category by the total number of cases (N) and multiply by 100.

Percentage distributions are tables that show the percentage of observations that fall into each category of the variable. Percentage distributions are routinely added to almost any frequency table and are especially important if comparisons between groups are to be considered.

Cumulative frequency distributions allow us to locate the relative position of a given score in a distribution.They are obtained by adding to the frequency in each category the frequencies of all the categories below it.

Cumulative percentage distributions have wider applications than cumulative frequency distributions. A cumulative percentage distribution is constructed by adding to the percentages in each category the percentages of all the categories below it.

One other method of expressing raw frequencies in relative terms is known as a rate. Rates are defined as the number of actual occurrences in a given time period divided by the number of possible occurrences. Rates are often multiplied by some power of 10 to eliminate decimal points and make the number easier to interpret.