Measures of Central Tendency
Researchers are often interested in defining a value that best describes
some attribute of the population. Often this attribute is a
measure of central tendency or a proportion.
Measures of Central Tendency
Several different measures of central tendency are defined below.

The mode is the most frequently appearing value in the
population or sample. Suppose we draw a sample of five women and measure their
weights. They weigh 100 pounds, 100 pounds, 130 pounds, 140 pounds, and 150
pounds. Since more women weigh 100 pounds than any other weight, the mode would
equal 100 pounds.

To find the median, we arrange the observations in order from
smallest to largest value. If there is an odd number of observations, the
median is the middle value. If there is an even number of observations, the
median is the average of the two middle values. Thus, in the sample of five
women, the median value would be 130 pounds; since 130 pounds is the middle
weight.

The mean of a sample or a population is computed by adding all
of the observations and dividing by the number of observations. Returning to
the example of the five women, the mean weight would equal (100 + 100 + 130 +
140 + 150)/5 = 620/5 = 124 pounds.
Proportions and Percentages
When the focus is on the degree to which a population possesses a
particular attribute, the measure of interest is a percentage or
a proportion.
 A proportion refers to the fraction of the total that
possesses a certain attribute. For example, we might ask what proportion of
women in our sample weigh less than 135 pounds. Since 3 women weigh less than
135 pounds, the proportion would be 3/5 or 0.60.

A percentage is another way of expressing a proportion. A
percentage is equal to the proportion times 100. In our example of the five
women, the percent of the total who weigh less than 135 pounds would be
100 * (3/5) or 60 percent.
Notation
Of the various measures, the mean and the proportion are
most important. The notation used to describe these measures appears below:

q: The proportion of elements in the sample that does not have a specified
attribute. Note that q = 1  p.
Note that capital letters refer to population
parameters, and lowercase letters refer to sample
statistics.