Average, Median, and Mode Guide

Learn how to measure central tendency, interpret averages, and avoid common mistakes.

Why averages can mislead

Averages are everywhere: salaries, grades, product ratings, and health metrics. But a single average can hide extreme values or uneven distributions. This guide explains when to use mean, median, or mode, and how to interpret results with context.

The three core measures

Mean: Sum of values divided by count.
Median: Middle value when sorted.
Mode: Most frequent value.

Each measure answers a different question. The mean tells you the balance point, the median gives the middle, and the mode shows the most common outcome. Use the one that fits the situation.

Worked examples

Suppose the values are 10, 12, 12, 13, and 50. The mean is (10 + 12 + 12 + 13 + 50) / 5 = 19.4. The median is 12, and the mode is 12. The mean is much higher because the outlier 50 skews the result.

In a salary dataset, this is common: one very high salary can lift the average, while the median shows a more realistic typical income. Use the median for skewed distributions.

When to use the mean

The mean is best when values are evenly distributed and outliers are rare. It is useful for totals, budgets, and performance metrics where every value matters equally.

When to use the median

The median is best for skewed data, such as housing prices, salaries, or wait times. It shows the middle and resists outliers.

When to use the mode

The mode is useful for categorical or repeated values. It answers "what is most common" and is helpful for inventory, sizes, or repeated outcomes.

Weighted averages

When values have different importance, use a weighted average. Multiply each value by its weight, sum the results, then divide by total weight.

Example: If homework is 40% and exams are 60%, a student with 90 on homework and 80 on exams has (90 * 0.4) + (80 * 0.6) = 84.

Common mistakes

Using mean when data is skewed.
Forgetting to sort data before finding median.
Assuming mode exists in every dataset.
Ignoring weights in weighted averages.

Practical checklist

Check for outliers before choosing a measure.
Use median for skewed data.
Use mean for balanced data.
Use mode for most common value or category.

Recommended calculators

References

Introductory statistics textbooks covering central tendency
Educational data analysis references for mean and median