Evidence-Based Practice for Nurses

FIGURE 13-6 Semiquartile Range of Age Data

Q 1 = 19 Median = 21 Q 3 = 22.5

1818 18 19 19 19 20 21 21 21 21 21 22 22 22 23 23 25 27 28

lies below the first quartile and three fourths of the data lie above it. The third

quartile value is the median of the upper half of the data; three fourths of the

data lie below the third quartile and one fourth of the data lies above it. The

semiquartile range is the difference between the third and first quartile values

and describes the middle half of a data distribution. In Figure 13-6, note that

50% of the data lie between 19 and 22.5, and the range is 3.5.

Percentile

A percentile is a measure of rank. Each percentile represents the percentage

of cases that a given value exceeds. The median is the 50th percentile, the first

quartile is the 25th percentile, and the third quartile is the 75th percentile

score in a given data set. For example, if a newborn baby boy’s weight is in the

39th percentile, he weighs more than 39% of babies tested weigh but less than

61% of the other babies.

Standard Deviation

The most commonly reported measure of variability is the standard deviation,

which is based on deviations from the mean of the data. Whereas the mean

is the expectation value (the expected “average” of the data set), the standard

deviation is the measure of the average deviations of a value from the mean in

a given data set. Because it is a measure of deviation from the mean, a standard

deviation should always be reported whenever a mean is reported. Standard

deviation is based on the normal curve and is used to determine the number

of data values that fall within a specific interval in a normal distribution. Un-

derstanding the standard deviation allows you to interpret an individual score

in comparison with all other scores in the data set. Recall the salary example

presented earlier. The data were variable because of the extreme ranges of

KEY TERMS

percentile: A

measure of rank

representing the

percentage of cases

that a given value

exceeds

standard deviation:

A measure of

variability used

to determine the

number of data

values falling

within a specific

interval in a normal

distribution

Consider how your ACT or SAT scores were reported. What was your raw score? What was your

percentile? What do these data indicate about your performance on these tests?

CRITICAL THINKING EXERCISE 13-1

346 CHAPTER 13 What Do the Quantitative Data Mean?