116 PART 3 Getting Down and Dirty with Data

arithmetic mean. (There are several other kinds of means besides the arithmetic

mean, which we describe later in this chapter.)

The mean of a sample is often denoted by the symbol m or by placing a horizontal

bar over the name of the variable, like X. The mean is obtained by adding up the

values and dividing by the sample size — meaning how many there are. (If you are

using software for this, make sure missing values are excluded, or the equation

will not compute.) Here’s a small sample of numbers — the diastolic blood pres-

sure (DBP) values of seven study participants (in mmHg) arranged in increasing

numerical order: 84, 84, 89, 91, 110, 114, and 116. For the DBP sample:

Arithmetic Mean 84 84 89 91 110 114 116 / 7

688 / 7

98.3 approximately

You can write the general formula for the arithmetic mean of N number of values

contained in the variable X in several ways:

Arithmetic Mean

m

X

X

N

N

X

N

i

i

i

N

i

X

1

See Chapter 2 for a refresher on mathematical notation and formulas, including

how to interpret the various forms of the summation symbol Σ (the Greek capital

sigma). In the rest of this chapter, we use the simplest form, meaning the form

without the i subscripts that refer to specific elements of an array, whenever

possible.

Some statistical books use the notation such that capital Xand capital N refer to

census parameters, and lowercase versions of those to refer to sample statistics.

In this book, we make it clear each time we present this notation whether we are

talking about a census or a sample.

Median

Like the mean, the median is a common measure of central tendency. In fact, it

could be argued that the median is the only one of the three that really takes the

word central seriously.

The median of a sample is the middle value in the sorted (ordered) set of numbers.

By definition, half of the numbers are smaller than the median, and half are larger.

The median of a population frequency distribution function (like the curves shown

in Figure 9-2) divides the total area under the curve into two equal parts: Half of

the area under the curve (AUC) lies to the left of the median, and half lies to

the right.

Consider the sample of diastolic blood pressure (DBP) measurements from seven

study participants from the preceding section. If you arrange the values in order