Quick Answer

For the data set {2, 3, 3, 5, 7}, the mean is 4, the median is 3, and the mode is 3.

Data Set

Separate values with commas, spaces, or newlines

Common Examples

Input	Result
2, 3, 3, 5, 7	Mean: 4, Median: 3, Mode: 3
10, 20, 30, 40, 50	Mean: 30, Median: 30, Mode: none
1, 1, 2, 2, 3	Mean: 1.8, Median: 2, Mode: 1, 2 (bimodal)
5, 10, 10, 10, 15, 20	Mean: 11.667, Median: 10, Mode: 10
100, 200, 300	Mean: 200, Median: 200, Mode: none

How It Works

Mean (Arithmetic Average)

The arithmetic mean is the sum of all values divided by the number of values.

Mean = (x₁ + x₂ + … + xₙ) / N

The mean is the most commonly used measure of central tendency. It accounts for every value in the data set, which means it can be influenced by outliers (extremely high or low values).

Median

The median is the middle value when the data is arranged in ascending order.

• For an odd number of values, the median is the value at position (N + 1) / 2.
• For an even number of values, the median is the average of the two middle values at positions N/2 and (N/2) + 1.

The median is less sensitive to outliers than the mean, making it a useful measure for skewed distributions. For example, median household income is often preferred over mean income because a few extremely high earners can skew the mean upward.

Mode

The mode is the value (or values) that appear most frequently in the data set.

• A data set has no mode if every value appears exactly once.
• A data set is unimodal if one value appears more often than all others.
• A data set is bimodal if two values tie for the highest frequency.
• A data set is multimodal if three or more values share the highest frequency.

Range

Range = Maximum value - Minimum value

The range is the simplest measure of spread and gives the total span of the data.

Worked Example

For the data set {4, 8, 6, 5, 3, 8, 9}:

Mean = (4 + 8 + 6 + 5 + 3 + 8 + 9) / 7 = 43 / 7 = 6.1429.

Median: Sort the data: {3, 4, 5, 6, 8, 8, 9}. There are 7 values (odd), so the median is the 4th value = 6.

Mode: The value 8 appears twice; all other values appear once. Mode = 8.

Range = 9 - 3 = 6.

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Frequently Asked Questions

What is the difference between mean, median, and mode?

The mean is the arithmetic average (sum divided by count). The median is the middle value in sorted order. The mode is the most frequently occurring value. All three measure the 'center' of a data set, but each responds differently to the shape of the distribution and to outliers.

When is the median more useful than the mean?

The median is more useful when the data is skewed or contains outliers. For example, in the set {1, 2, 3, 4, 100}, the mean is 22 but the median is 3. The median better represents the typical value because the outlier (100) pulls the mean far from the center of most of the data.

Can a data set have more than one mode?

Yes. A data set is bimodal if two values tie for the highest frequency, and multimodal if three or more do. For example, in {1, 1, 2, 3, 3}, both 1 and 3 appear twice, making the data set bimodal.

What if all values in the data set are the same?

If every value is identical, the mean, median, and mode are all equal to that value, and the range is 0.

Does this calculator support decimal values?

Yes. Enter decimal numbers just as you would whole numbers. For instance, entering 1.5, 2.7, 3.1 computes the mean as 2.4333, the median as 2.7, and the mode as none (since no value repeats).