Direct answer
Use the mean for additive numerical balance, the median for an ordered midpoint resistant to extremes, and the mode for the most frequent value or category; the data and question determine which center is meaningful.
Visual explanation
How an extreme value changes measures of center
What this calculation tells you
Measures of center answer different questions. The mean is the balance point, the median divides ordered observations in half, and the mode identifies the most frequent exact value or label.
Ask whether distances between values are meaningful, whether extreme observations should influence the summary, and whether the practical question concerns a balance point, a middle position, or the most common outcome.
Where it is used
Household and finance
Distinguish a typical cost from an equal-share arithmetic balance.
Public reporting
Explain why incomes or waiting times often use medians.
Inventory
Identify the most frequently requested size or category.
Research
Choose a center compatible with the measurement scale and model.
Common situations
- Summarizing a skewed price distribution.
- Finding the middle response on an ordered scale.
- Identifying the most common category.
- Explaining why two published averages disagree.
Start with the statistical question
Ask whether distances between values are meaningful, whether extreme observations should influence the summary, and whether the practical question concerns a balance point, a middle position, or the most common outcome.
A movable high observation pulls the mean along a number line while the median remains on the middle observation. A frequency stack separately shows how the mode is determined by repetition.
Worked example
For household repair bills of 40, 45, 50, 55, and 510, the mean is 140 while the median is 50. Both are correct, but the median better describes a typical bill and the mean better describes total cost divided equally across five bills.
Assumptions that carry the result
The mean requires numerical values on a scale where addition and division are meaningful. The median requires an ordered scale. The mode can describe nominal categories but exact numeric modes may change after rounding.
Interpret the result without overreaching
A center says nothing about spread, subgroup structure, sample quality, or future outcomes. Report the measure by name and pair it with sample size and an appropriate measure of variability.
- Calling every center an average without naming it.
- Using the mean for unordered categories.
- Treating a multimodal distribution as one homogeneous group.
Practical questions
Frequently asked questions
Is the median always better when data are skewed?
It is often more representative of a typical ordered observation, but the mean may still answer an additive or resource-allocation question.
Can there be two modes?
Yes. Any values tied for the greatest frequency are modes when that frequency exceeds the others.
Does mean greater than median prove right skew?
No. It can be a clue, but the full distribution and sample context must be inspected.
Further reading
Authoritative sources
Use these primary and professional resources to check definitions, conventions, or requirements that may extend beyond this guide.