Russel-Research-Method-in-Anthropology

170 Chapter 7
The Normal Curve and z-Scores
The so-called normal distribution is generated by a formula that can be
found in many intro statistics texts. The distribution has a mean of 0 and a
standard deviation of 1. The standard deviation is a measure of how much
the scores in a distribution vary from the mean score. The larger the standard
deviation, the more dispersion around the mean. Here’s the formula for the
standard deviation, or sd. (We will take up the sd again in chapter 19. The sd
is the square root of the variance, which we’ll take up in chapter 20.)
sd 2
x x
n 1
Formula 7.1
The symbol x (read: x-bar) in formula 7.1 is used to signify the mean of a
sample. The mean of a population (the parameter we want to estimate), is
symbolized by μ (the Greek lower-case letter ‘‘mu,’’ pronounced ‘‘myoo’’).
The standard deviation of a population is symbolized by σ (the Greek lowercase
letter ‘‘sigma’’), and the standard deviation of a sample is written as SD
or sd or s. The standard deviation is the square root of the sum of all the
squared differences between every score in a set of scores and the mean,
divided by the number of scores minus 1.
The standard deviation of a sampling distribution of means is the standard
error of the mean, or SEM. The formula for calculating SEM is:
SEM sd
n
Formula 7.2
where n is the sample size. In other words, the standard error of the mean
gives us an idea of how much a sample mean varies from the mean of the
population that we’re trying to estimate.
Suppose that in a sample of 100 merchants in a small town in Malaysia,
you find that the average income is RM12,600 (about $3,300 in 2005 U.S.
dollars), with a standard deviation of RM4,000 (RM is the symbol for the
Malaysian Ringgit). The standard error of the mean is:
Do the calculation:
12,600 4,000 12,600 400
100
12,600 400 13,000
12,600 400 12,200