Social Research Methods: Qualitative and Quantitative Approaches

ANALYSIS OF QUANTITATIVE DATA

lowest. If most cases have higher scores with a few
extreme low scores, the mean will be the lowest, the
median in the middle, and the mode the highest. In
general, the median is best to use for a skewed dis-
tribution, although the mean is used in most other
statistics (see Figure 3).

Measures of Variation

The measure of central tendency is a single-number
summary of a distribution; however, the measures
give only its center. Another characteristic of a dis-
tribution is its spread, dispersion,or variability
around the center. Two distributions can have iden-
tical measures of central tendency but differ in their
spread about the center. For example, seven people
are at a bus stop in front of a bar. Their ages are 25,
26, 27, 30, 33, 34, 35. Both the median and the

mean are 30. At a bus stop in front of an ice cream

store, seven people have the identical median and

mean, but their ages are 5, 10, 20, 30, 40, 50, 55.

The ages of the group in front of the ice cream store

are spread more from the center, or the distribution

has more variability.

Variabilityhas important social implications.

For example, in city X, the median and mean fam-

ily income is $37,600 per year, and it has zero vari-

ation. Zero variationmeans that every family has

an income of exactly $37,600. City Y has the same

median and mean family income, but 96 percent of

its families have incomes of $14,000 per year and

4 percent have incomes of $350,000 per year. City

X has perfect income equality whereas there is great

inequality in city Y. If we do not know the variabil-

ity of income in the two cities, we miss very impor-

tant information.

We measure variation in three ways: range, per-

centile, and standard deviation. Rangeis the sim-

plest. It consists of the largest and smallest scores.

For example, the range for the bus stop in front of

the bar is from 25 to 35, or 35  25 10 years. If

FIGURE 3 Measures of Central Tendency

Skewed Distributions

Normal Distribution

Mode Median Mean MeanMedianMode

Number of

Cases Mean, Median, Mode

Lowest Values of Variables Highest

Range A measure of dispersion for one variable indi-

cating the highest and lowest scores.