Central Tendency

Properties of the Mode

--Not sensitive to outliers. -Only measure of central tendency that can be used with nominal data. -Least reliable measure due to high variability across populations

Properties of the Mean

-Most sensitive to outliers than other measures of central tendency -Most reliable measure -Requires division and often results in a fraction.

Properties of the Median

-Somewhat sensitive to outliers -Preferred measure when the distribution is strongly skewed since it is not as sensitive to outliers

Unimodal and Approximately Symmetrical

Mean, median, and mode are approximately equal

Unimodal and Perfectly Symmetrical

Mean, median, and mode are equal

(N+1)/2

Median Location

Mode

Most frequently occurring score in a distribution -Simplest and least useful measure of central tendency -Possible to have more than one

Mode > Median > Mean -The MEAN is pulled toward the corresponding tail to balance the distribution

Negatively Skewed Distribution

Mean > Median > Mode -The MEAN is pulled toward the corresponding tail to balance the distribution

Positively Skewed Distribution

Median

Score that divides the distribution in half, such that half of the scores are greater and half of the scores are less than the median

Mean

Should not be used as a measure of central tendency for discrete data

Mean

The average of the distribution -The best measure of central tendency