š Free Statistics Tool
Average
Calculator
Mean, median, mode, standard deviation & more ā enter any numbers and get the full picture instantly.
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Ā· Space
āµ Newline
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Understanding the Statistics
š Mean (Average)
The sum of all values divided by the count. Most common measure of central tendency. Sensitive to outliers.
Ī£x Ć· n
š Median
The middle value when numbers are sorted. Robust to outliers ā great for skewed data like income or home prices.
Middle value of sorted list
šÆ Mode
The most frequently occurring value. A dataset can have multiple modes or none if all values appear equally.
Most frequent value(s)
š Range
The difference between the maximum and minimum values. Simple measure of spread but sensitive to outliers.
Max ā Min
ć½ļø Std Deviation
Measures how spread out values are from the mean. Low = tightly clustered, High = widely spread.
ā(Ī£(xāĪ¼)Ā² Ć· n)
š Variance
Standard deviation squared. Represents the average of squared differences from the mean in the data set.
ĻĀ² = Ī£(xāĪ¼)Ā² Ć· n
Frequently Asked Questions
When should I use median instead of mean? ā¾
Use median when your data is skewed or has outliers. For example, average household income uses median because a few billionaires would wildly inflate the mean. If data is roughly symmetric with no extreme outliers, mean and median will be similar.
Can a data set have no mode? ā¾
Yes. If every value appears exactly once, there is no mode. A dataset can also be bimodal (two modes) or multimodal (many modes) if multiple values tie for the highest frequency.
What is the difference between population and sample standard deviation? ā¾
Population std deviation (Ļ) divides by n and is used when you have data for the entire population. Sample std deviation (s) divides by nā1 and is used when your data is a sample meant to represent a larger group. Our calculator uses population std deviation (Ć·n).
How do I calculate the average of percentages? ā¾
Simply enter the percentages as numbers (e.g., 75, 82, 91) and calculate the mean. This is a simple average. For a weighted average of percentages (where groups are different sizes), you’d need to weight each percentage by its group size, which requires additional data.