Overview: What Are Measures of Central Tendency?
Measures of central tendency represent the most typical score or value in a group of scores on some measure in either a population or a sample of that population. Along with measures of variability, they convey much information about a distribution. The three most common measurements are the mean, median, and mode.
What is the Mean?
The mean is the average value of all the numbers in the data set, and is a representation of the population mean. It is computed by summing all values in the data set, and dividing by the number of values. Many statistical calculations use the mean value to determine if treatment conditions have had an effect by comparing the mean of a pretreatment sample with a post treatment sample.
What Is the Median?
The median is the value in the middle if all the numbers in a data set are arranged from largest to smallest. It is often reported rather than the mean value , if the values between the largest value and the smallest value are widely separated, such as with salaries or the price of housing in a community, This is because the median is less affected by extreme values. When calculating the median, first arrange the values from largest to smallest, listing all instances of a value as many times as it occurs. Suppose the president of a company makes $200,000 a year, the vice president makes $50,000 a year, 2 supervisors make $25,000 a year, 4 sales representatives make $21,000 a year, 2 custodians and 2 warehouse workers make $15,000 a year, and 3 clerical workers make $12,000 a year. The median salary is $21,000.
What is the Mode?
The mode is the measure that occurs most frequently. In the above example, there are 2 modes, the salary of the 4 sales representatives of $21,000, and the salary of the 2 warehouse workers and 2 custodians, at $15,000. It is not as useful as a measure of central tendency because it can be affected by scores that are not the center of the data set, but are in other places in the data set. If a third warehouse worker were hired at $15,000, the new mode would be below the mean or the median.
Which Measure Is the Most Useful?
If a distribution has only one mode and is symmetric, such as the normal curve that reflects scores on the SAT and ACT, the mean will be the most useful. If there is a large difference between the mean and the median, as when a distribution has many scores that are higher than the mean or lower than the mean, the median may be the most useful. It is less affected by outlying scores, and may give a better picture than the mean. However, the mean is most often used in many other statistical measures and is the most often reported.
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