Why are the measures of central tendency like mean, median and mode important in research?

Central Tendency. The central
tendency of a distribution is an estimate of the "center" of a distribution of values.
There are three major types of estimates of central
tendency:

• Mean
  


• Median


• Mode
  

The Mean or
average is probably the most commonly used method of describing central tendency. To
compute the mean all you do is add up all the values and divide by the number of values.
For example, the mean or average quiz score is determined by summing all the scores and
dividing by the number of students taking the exam. For example, consider the test score
values:

15, 20, 21, 20, 36, 15, 25,
15

The sum of these 8 values is 167, so the
mean is 167/8 = 20.875.

The
Median is the score found at the exact middle of the set of
values. One way to compute the median is to list all scores in numerical order, and then
locate the score in the center of the sample. For example, if there are 500 scores in
the list, score #250 would be the median. If we order the 8 scores shown above, we would
get:

15,15,15,20,20,21,25,36

There
are 8 scores and score #4 and #5 represent the halfway point. Since both of these scores
are 20, the median is 20. If the two middle scores had different values, you would have
to interpolate to determine the median.

The
mode is the most frequently occurring value in the set of
scores. To determine the mode, you might again order the scores as shown above, and then
count each one. The most frequently occurring value is the mode. In our example, the
value 15 occurs three times and is the model. In some distributions there is more than
one modal value. For instance, in a bimodal distribution there are two values that occur
most frequently.

Notice that for the same set of 8 scores
we got three different values -- 20.875, 20, and 15 -- for the mean, median and mode
respectively. If the distribution is truly normal (i.e., bell-shaped), the mean, median
and mode are all equal to each other.

The
Standard Deviation is a more accurate and detailed estimate
of dispersion because an outlier can greatly exaggerate the range (as was true in this
example where the single outlier value of 36 stands apart from the rest of the values.
The Standard Deviation shows the relation that set of scores has to the mean of the
sample. Again lets take the set of scores: