Introductory Biostatistics

we are now able to define a number of important summarized measures, start-
ing with the arithmetic average ormean.

2.2.1 Mean

Given a data set of sizen,

fx 1 ;x 2 ;...;xng

the mean of thex’s will be denoted byx(‘‘x-bar’’) and is computed by sum-
ming all thex’s and dividing the sum byn. Symbolically,

x¼

P

x

n

It is important to know thatS(‘‘sigma’’) stands for an operation (that of
obtaining the sum of the quantities that follow) rather than a quantity itself.
For example, considering the data set

f 8 ; 5 ; 4 ; 12 ; 15 ; 5 ; 7 g

we have

n¼ 7

X

x¼ 56

leading to

x¼

56

7

¼ 8

Occasionally, data, especially secondhand data, are presented in the grouped
form of a frequency table. In these cases, the meanxcan be approximated
using the formula

xF

P

ðfmÞ

n

wherefdenotes the frequency (i.e., the number of observations in an interval),
mthe interval midpoint, and the summation is across the intervals. The mid-
point for an interval is obtained by calculating the average of the interval lower
true boundary and the upper true boundary. For example, if the first three

NUMERICAL METHODS 73