Mean Formula

The Formula

\mu = \frac{\sum x}{n}

When to use: Imagine redistributing all the data equally — the mean is the value each person would get if everyone shared equally. It is the balance point of the data.

Quick Example

Test scores: 80, 90, 85, 75, 95. \text{Mean} = (80 + 90 + 85 + 75 + 95) / 5 = 85

Notation

\bar{x} for sample mean, \mu for population mean

What This Formula Means

The arithmetic mean (average) of a data set is the sum of all values divided by the number of values.

Imagine redistributing all the data equally — the mean is the value each person would get if everyone shared equally. It is the balance point of the data.

Formal View

\bar{x} = \frac{1}{n}\sum_{i=1}^{n} x_i for a sample \{x_1, x_2, \ldots, x_n\}

Worked Examples

Example 1

easy
Find the arithmetic mean of the data set: \{4, 8, 15, 16, 23\}.

Solution

  1. 1
    Add all values: 4 + 8 + 15 + 16 + 23 = 66.
  2. 2
    Count the number of values: n = 5.
  3. 3
    Divide the sum by n: \bar{x} = \frac{66}{5} = 13.2.

Answer

\bar{x} = 13.2
The arithmetic mean is the sum of all values divided by the number of values. It represents the central tendency of a data set and is sensitive to extreme values (outliers).

Example 2

medium
A student scored 72, 85, 90, 68, and 95 on five tests. What score does she need on the sixth test to achieve a mean of 85?

Common Mistakes

  • Dividing the sum by the wrong count — forgetting to include zero values in the total count
  • Confusing mean with median — the mean is the arithmetic average, not the middle value
  • Assuming the mean must be one of the data values — it can be a value not in the dataset

Why This Formula Matters

The mean is the most common summary statistic in science, economics, and everyday life — it compresses a whole data set into one representative number.

Frequently Asked Questions

What is the Mean formula?

The arithmetic mean (average) of a data set is the sum of all values divided by the number of values.

How do you use the Mean formula?

Imagine redistributing all the data equally — the mean is the value each person would get if everyone shared equally. It is the balance point of the data.

What do the symbols mean in the Mean formula?

\bar{x} for sample mean, \mu for population mean

Why is the Mean formula important in Math?

The mean is the most common summary statistic in science, economics, and everyday life — it compresses a whole data set into one representative number.

What do students get wrong about Mean?

Mean of 1, 2, 3, 100 is 26.5—not representative because of the outlier.

What should I learn before the Mean formula?

Before studying the Mean formula, you should understand: addition, division.

← Back to Mean See All Examples Practice Problems