HP 50G, User Manual

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Page 18-3
Example 1 -- For the data stored in the previous example, the single-variable
statistics results are the following:
Mean: 2.13333333333, Std Dev: 0.964207949406,
Variance: 0.929696969697
Total: 25.6, Maximum: 4.5, Minimum: 1.1
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,
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:
∑
=
⋅ =
n
i
i
x
n
x
1
.
1
.
1 1
,
1
2 1
∑
=
= ⋅ =
n
i
i h
n
n g
x x
x x x x L