Statistics

Measures Of Central Tendency

Both statisticians and non-statisticians talk about "averages" all the time. But the term average can have a number of different meanings. In the field of statistics, therefore, workers prefer to use the term "measure of central tendency" for the concept of an "average." One way to understand how various measures of central tendency (different kinds of "average") differ from each other is to consider a classroom consisting of only six students. A study of the six students shows that their family incomes are as follows: \$20,000; \$25,000; \$20,000; \$30,000; \$27,500; \$150,000. What is the "average" income for the students in this classroom?

The measure of central tendency that most students learn in school is the mean. The mean for any set of numbers is found by adding all the numbers and dividing by the quantity of numbers. In this example, the mean would be equal to (\$20,000 + \$25,000 + \$20,000 + \$30,000 + \$27,500 + \$150,000) ÷ 6 = \$45,417. But how much useful information does this answer give about the six students in the classroom? The mean that has been calculated (\$45,417) is greater than the household income of five of the six students.

Another way of calculating central tendency is known as the median. The median value of a set of measurements is the middle value when the measurements are arranged in order from least to greatest. When there are an even number of measurements, the median is half way between the middle two measurements. In the above example, the measurements can be rearranged from least to greatest: \$20,000; \$20,000; \$25,000; \$27,500; \$30,000; \$150,000. In this case, the middle two measurements are

 Improved Not Improved Total Experimental Group 62 38 100 Control Group 45 55 100 Total 107 93 200

\$25,000 and \$27,500, and half way between them is \$26,250, the median in this case. You can see that the median in this example gives a better view of the household incomes for the classroom than does the mean.

A third measure of central tendency is the mode. The mode is the value most frequently observed in a study. In the household income study, the mode is \$20,000 since it is the value found most often in the study. Each measure of central tendency has certain advantages and disadvantages and is used, therefore, under certain special circumstances.