Representation of Data
Data are often represented in frequency distributions, which indicate
the frequency of each score in a set of scores. Sociologists also use
graphs to represent data. These include pie graphs, frequency
histograms, frequency polygons, and line graphs. Line graphs are
important in representing the results of experiments, because they are
used to illustrate the relationship between independent and dependent
Descriptive statistics summarize and organize research data. Measures
of central tendency represent the typical score in a set of scores. The
mode is the most frequently occurring score, the median is the middle
score, and the mean is the arithmetic average of the set of scores.
Measures of variability represent the degree of dispersion of scores.
The range is the difference between the highest and lowest scores. The
variance is the average of the squared deviations from the mean of the
set of scores. And the standard deviation is the square root of the
Many kinds of measurements fall on a normal, or bell-shaped, curve.
A certain percentage of scores fall below each point on the abscissa of
the normal curve. Percentiles identify the percentage of scores that fall
below a particular score.
Correlational statistics assess the relationship between two or more
sets of scores. A correlation may be positive or negative and vary from
0.00 to plus or minus 1.00. The existence of a correlation does not
necessarily mean that one of the correlated variables causes changes in
the other. Nor does the existence of a correlation preclude that
possibility. Correlations are commonly graphed on scatter plots.
Perhaps the most common correlational technique is the Pearson's
product-moment correlation. You square the Pearson's
product-moment correlation to get the coefficient of determination,
which will indicate the amount of variance in one variable accounted
for by another variable.
Inferential statistics permit social researchers to determine whether their
findings can be generalized from their samples to the populations they
represent. Consider a simple investigation in which an experimental
group that is exposed to a condition is compared with a control group
that is not. For the difference between the means of the two groups to
be statistically significant, the difference must have a low probability
(usually less than 5 percent) of occurring by normal random variation.