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Mean Median Mode Range Calculator

Calculate mean, median, mode, and range from dataset with explanations.

statistics-mmmr
Statistical Analysis
Mean (Average)
Median (Middle)
Mode (Most Frequent)
Range (Max - Min)
Data Count
Sum

Statistical Formulas

Mean: (sum of all values) / (count)

Median: Middle value when ordered

Mode: Most frequently occurring value

Range: Maximum - Minimum

When to Use Each Statistic

StatisticBest ForWeakness
MeanSymmetric dataAffected by outliers
MedianSkewed dataIgnores some values
ModeCategorical dataMay not exist
RangeQuick spreadOnly uses extremes

Frequently Asked Questions

What is the mean (average)?

Sum all values, divide by count. Mean = (sum of all data) / (number of values). Example: {2,3,5,7,3} → sum=20, count=5 → mean=4.

What is the median?

Middle value when data is ordered. If odd count, it's the middle. If even count, it's the average of two middle values. Example: {2,3,5} → median=3. {2,3,5,7} → median=(3+5)/2=4.

What is the mode?

Most frequently occurring value. Can have one mode, multiple modes, or no mode. Example: {2,3,3,5,7,3} → mode=3 (appears 3 times).

What is the range?

Difference between highest and lowest values. Range = max - min. Example: {2,3,5,7} → range = 7-2 = 5.

When is mean best to use?

When data is symmetric and has no extreme outliers. Affected by all values. Good for normally distributed data.

When is median best to use?

When data has outliers or is skewed. Median is resistant to extreme values. Better for asymmetric distributions.

When is mode best to use?

For categorical data or to find most common value. Useful when frequency matters more than averages. Good for non-numeric data.

What if there are multiple modes?

Bimodal (2 modes) or multimodal (3+ modes) are possible. Data has multiple peaks. Can indicate distinct groups.

How do outliers affect mean vs median?

Mean is heavily affected by outliers. Median ignores extreme values. Example: {1,2,3,4,100} → mean=22, median=3.

Why is range limited as a measure?

Range only uses max and min, ignoring all middle values. Doesn't show distribution. Larger datasets needed to avoid anomalies.

What is the relationship between mean, median, mode?

In symmetric distribution: mean ≈ median ≈ mode. In skewed distribution: they differ. Comparison shows data shape.

How do I find these for grouped data?

Grouped data requires finding class midpoints and weighted calculations. More complex than raw data but same concepts apply.