Numerical Measures of Central Tendency and Variability
Read these sections and complete the questions at the end of each section. First, we will define central tendency and introduce mean, median, and mode. We will then elaborate on median and mean and discusses their strengths and weaknesses in measuring central tendency. Finally, we'll address variability, range, interquartile range, variance, and the standard deviation.
Measures of Central Tendency
The median is also a frequently used measure of central tendency. The median is the midpoint of a distribution: the same number of scores is above the median as below it. For the data in Table 1, there arescores. The 16th highest score (which equals ) is the median because there are scores below the score and scores above the score. The median can also be thought of as the percentile.
Computation of the Median
When there is an odd number of numbers, the median is simply the middle number. For example, the median of , , and is . When there is an even number of numbers, the median is the mean of the two middle numbers. Thus, the median of the numbers is . When there are numbers with the same values, then the formula for the third definition of the percentile should be used.