Page 18-3
Definitions
The definitions
used for these quantities are the following:
Suppose that you have a number data points x
1
, x
2
, x
3
, …, representing
different measurements of the same discrete or continuous variable x. The set
of all possible values of the quantity x is referred to as the population of x. A
finite population will have only a fixed number of elements x
i
. If the quantity x
represents the measurement of a continuous quantity, and since, in theory,
such a quantity can take an infinite number of values, the population of x in
this case is infinite. If you select a sub-set of a population, represented by
the n data values {x
1
, x
2
, …, x
n
}, we say you have selected a sample of values
of x.
Samples are characterized by a number of measures or statistics. There are
measures of central tendency, such as the mean, median, and mode, and
measures of spreading, such as the range, variance, and standard deviation.
Measures of central tendency
The mean (or arithmetic mean) of the sample,
x, is defined as the average
value of the sample elements,
∑
=
⋅
=
n
i
i
x
n
x
1
.
1
The value labeled
Total
obtained above represents the summation of the
values of x, or
Σ
x
i
= n
⋅
x. This is the value provided by the calculator under
the heading
Mean
. Other mean values used in certain applications are the
geometric mean, x
g
, or the harmonic mean, x
h
, defined as:
.
1
1
,
1
2
1
∑
=
=
⋅
=
n
i
i
h
n
n
g
x
x
x
x
x
x
L
Examples of calculation of these measures, using lists, are available in
Chapter 8.
The median is the value that splits the data set in the middle when the
elements are placed in increasing order. If you have an odd number, n, of
ordered elements, the median of this sample is the value located in position
