Evidence-Based Practice for Nurses

A number of human traits, such as intelligence and height, are considered to

be normally distributed in the population.

When Data Are Not Normally Distributed

Often data do not fit a normal distribution and are considered to be asymmetric

or skewed. In asymmetric distributions, the peak of the data is not at the center

of the distribution, and one tail is longer than the other. Skewed distributions

are usually discussed in terms of their direction. If the longer tail is pointing to

the left, the data are considered to be negatively skewed (Figure 13-3). In this

situation, the mean is less than the median and mode. For example, a group

of students take a test for which all but one student studied. The one student,

who did not study, scores very low. This low score, because it is an outlier, af-

fects the mean because the scores of students who studied are high. This outlier

contributes to a negatively skewed distribution. The low score pulls down the

mean and pulls with it the tail of the distribution to the left. If the mean is

greater than the median and mode, then the data are positively skewed, pulling

the tail to the right. For example, an instructor gives a difficult test. Only one

or two students scored high on the test. The rest of the students’ scores were

low. Most students’ scores are lower than the mean because the outliers affect

the mean. The distribution of these scores is positively skewed. The extremely

high scores pull up the mean and pull the tail in a positive direction toward

the right (Figure 13-4).

Attention should be given to how the data are spread, or dispersed, around

the mean. Just as schoolchildren or military personnel wear uniforms to be

like each other, uniform data have very little spread and look like each other.

Normal (symmetric) distribution

Mean = Median = Mode

FIGURE 13-2 Example of a Normal Distribution

KEY TERMS

skewed: An

asymmetrical

distribution of data

negatively skewed:

A distribution when

the mean is less

than the median

and the mode;

the longer tail is

pointing to the left

positively skewed:

Distribution when

the mean is greater

than the median

and the mode;

the longer tail is

pointing to the right

342 CHAPTER 13 What Do the Quantitative Data Mean?