Mean, Median, Mode Calculator – Statistics Calculator Online

Calculate mean, median, and mode of any dataset with our free online statistics calculator. Enter your numbers and get comprehensive central tendency measures instantly.

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Examples:

Understanding Central Tendency

Central tendency measures tell you where the "center" of your data lies. The mean (average), median (middle value), and mode (most frequent value) each describe the center differently. Which one you use depends on your data's characteristics and what question you're trying to answer.

The mean uses all values but is sensitive to outliers. The median ignores extreme values and represents the true middle. The mode tells you what's most common. Together, they give a complete picture of your data's center.

Formulas and Methods

Mean (Average)

Mean = Sum / Count

Add all values, divide by how many

Median (Middle)

Sort, find middle value

For even count: average of two middle

Mode (Most Frequent)

Value with highest frequency

Can have multiple modes or none

Worked Examples

Example 1: Test Scores

Data: 85, 90, 78, 92, 88

Sorted: 78, 85, 88, 90, 92

Mean = (78+85+88+90+92)/5 = 433/5 = 86.6

Median = 88 (middle value)

Mode = None (all values appear once)

Example 2: With Outlier

Data: 10, 12, 11, 13, 12, 100, 14

Sorted: 10, 11, 12, 12, 13, 14, 100

Mean = 172/7 = 24.6 (pulled up by 100)

Median = 12 (resistant to outlier)

Mode = 12 (appears twice)

Example 3: Multiple Modes

Data: 2, 2, 3, 3, 4, 4, 5

Frequencies: 2→2, 3→2, 4→2, 5→1

Mean = 23/7 = 3.29

Median = 3

Mode = 2, 3, 4 (trimodal)

Example 4: Even Count

Data: 5, 8, 3, 9, 7, 6

Sorted: 3, 5, 6, 7, 8, 9

Mean = 38/6 = 6.33

Median = (6+7)/2 = 6.5 (average of two middle)

Mode = None

Quick Fact

The word "average" usually means the arithmetic mean, but there are actually dozens of different "averages" in mathematics. The geometric mean (nth root of product) is used for growth rates. The harmonic mean is used for rates like speed. The median is technically also an average!

Frequently Asked Questions

When should I use mean vs median?

Use the mean for symmetric data without outliers – it uses all information. Use the median for skewed data or when outliers exist – it's resistant to extreme values. House prices and salaries are typically reported as medians for this reason.

Can a dataset have no mode?

Yes! If every value appears exactly once, there's no mode. Some datasets also have multiple modes (bimodal, trimodal, etc.) when several values tie for most frequent.

Why is the mean higher than the median?

When mean > median, your data is right-skewed (positive skew). High outliers pull the mean up while the median stays put. Income data often shows this pattern – a few very high incomes raise the mean above the median.

What does IQR tell me?

The Interquartile Range (Q3 - Q1) shows the spread of the middle 50% of your data. Unlike the full range, IQR ignores outliers. A small IQR means the middle values are clustered; a large IQR means they're spread out.

How do quartiles work?

Q1 (first quartile) has 25% of data below it. Q2 is the median (50% below). Q3 (third quartile) has 75% below. These divide your data into four equal parts, helping you understand the distribution shape.

What if my dataset is very small?

With fewer than 4-5 values, measures like quartiles become less meaningful. The mean and median still work, but interpret them cautiously. Small samples are highly variable and may not represent the population well.

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