CHAPTER 9 Summarizing and Graphing Your Data 119

to calculate the GM using this formula, you take the log of each value in your

sample, then average all those logs together, and then take the antilog of that

average. You can choose to use either natural or common logarithms, but make

sure that whatever you choose, you use same type of antilog. (Flip to Chapter 2 for

the basics of logarithms.)

Describing the spread of your data

After central tendency (described earlier in “Locating the center of your data”),

the second most important set of summary statistics for numerical values refers

to how tightly or loosely they tend to cluster around a central value, meaning how

they are dispersed. There are several common measures of dispersion, as you find

out in the following sections.

Standard deviation, variance, and

coefficient of variation

The standard deviation (usually abbreviated SD, sd, or just s) of a set of numerical

values tells you how much the individual values tend to differ from the mean in

either direction (see “Locating the center of your data” for a discussion of the

mean). The SD is calculated as follows:

SD

sd

s

d

N

d

X

X

i

i

i

(

1 ^where

2

i

)

This formula is saying that you calculate the SD of a set of N numbers by first

subtracting the mean from each value (Xi) to get the deviation (di) of each value

from the mean. Then, you take the square each of these deviations and add up the

di

2 terms. After that, you divide that number by N  – 1, and finally, you take

the square root of that number to get your answer, which is the SD.

For the sample of diastolic blood pressure (DBP) measurements for seven study

participants in the example used earlier in this chapter, where the values are 84,

84, 89, 91, 110, 114, and 116 mmHg and the mean is 98.3 mmHg, you calculate the

SD as follows:

SD

(

. )

(

. )

...

(

. )

84

98 3

84

98 3

116

98 3

7

1

14

2

2

2

.4

Several other useful measures of dispersion are related to the SD:»

» ^{Variance: The variance is just the square of the SD. For the DBP example, the}

variance 14 4

207 36

2

.

.

.