Averages or measures
of central tendency are:
1. Mean The number found by adding
the data and then dividing by the number of data
values.
2. Median The middle number when the
numbers in the data values are arranged in order
of size. If there are two middle numbers (in the
case of an even number of
data), the median is the mean of the two middle numbers.
3. Mode The value that occurs most
frequently. If no number occurs more than once,
there is
no mode. It is possible to have more than one mode.
The mean is the most sensitive average.
It reflects the entire distribution and is the most common
average. The median gives the middle value.
It is useful when there are a few extraordinary values
to distort the mean. The mode is the average
that measures "popularity." It is possible to have
no mode or more than one mode.
Measures of position include quartiles, deciles, and
percentiles.
Measures of dispersion include the range, variance,
and standard deviation.
The standard deviation of a sample, denoted by
s, is the square root of the variance. To
find it, carry out these steps:
1. Determine
the mean of the set of numbers.
2. Subtract
the mean from each number in the set.
3. Square each
of these differences.
4. Find the
sum of the squares of the differences.
5. Divide this
sum by one less than the number of pieces of data.
This is the variance of the sample.
6. Take
the square root of the variance.
This is the standard deviation of the sample.
