Learning Objective

At the end of this section, the learner will be able to define mean, median, and mode; calculate each from a dataset; and determine which measure best represents central tendency in normal and skewed distributions.

Mean

The mean, or arithmetic average, is obtained by dividing the sum of all observations by the total number of observations. It is widely used but can be influenced by extreme values (outliers).

Median

The median is the midpoint of an ordered dataset, dividing the group into equal upper and lower halves. The value below which 50% of observations fall represents the 50th percentile. The median is more robust when data are skewed or contain outliers.

Mode

The mode refers to the most frequently occurring value in the dataset. A dataset may have one mode (unimodal), more than one (bimodal or multimodal), or none.

Example

For the dataset:
3, 6, 7, 7, 9, 10, 12, 15, 16

• Mode = 7
• Median = 9
• Mean = 9.4

This illustrates how the three measures may differ even when describing the same data.

Effect of Skewness

Not all distributions are symmetrical. In skewed distributions, the measures of central tendency may shift:

• Positive skew (tail to the right): mean > median
• Negative skew (tail to the left): median > mean

For skewed data, the median generally provides a more accurate representation of central tendency than the mean.

Activity

Activity