How to Calculate the Mean: Steps, Examples & Formula

Whether you’re analyzing test scores, tracking monthly expenses, or working through a statistics problem set, calculating the mean is one of those skills that pays off over and over. The good news? The math behind it is straightforward — even if the data comes wrapped in a frequency table. This guide walks you through the mean formula step-by-step, shows you how to solve the exact examples people search for most, and explains how the process changes when you add frequencies or grouped intervals.

Formula: Sum of values divided by count · Example 1: Mean of 5, 11, 2, 12, 4, 2 is 6 · Example 2: Mean of 4, 6, 8, 10, 12, 14 is 9 · Example 3: Mean of 3, 4, 5, 6, 7 is 5 · Frequency table: ∑(fx) / ∑f

How do you calculate mean?

The mean is what most people call the “average” — the number you get when you spread the total evenly across all data points. According to the Khan Academy (Statistics Education Platform), the mean is “the average number; found by adding all data points and dividing by the number of data points.”

The three-step process

• Add up all data values. Sum every number in your dataset.
• Count the number of values. This is your sample size, often written as n.
• Divide the sum by the count. This gives you the mean.

The formula looks like this: Mean = ∑x / n, where ∑x is the sum of all values. LibreTexts (Open Statistics Textbook) uses this exact notation in its formal treatment of measures of central tendency.

What is the mean of 5, 11, 2, 12, 4, 2?

This exact example appears frequently in search results, so let’s work through it completely. According to CalculatorSoup (Online Statistics Calculators), the steps for any mean calculation are the same — it’s just the numbers that change.

Step-by-step calculation

1. Add all values: 5 + 11 + 2 + 12 + 4 + 2 = 36
2. Count the values: There are 6 numbers in the list
3. Divide: 36 ÷ 6 = 6

Verification

The mean of 5, 11, 2, 12, 4, and 2 is 6. You can check this by redistributing: if each value were 6, the total would be 6 × 6 = 36 — matching our sum. The math checks out.

How to calculate a mean, median, and mode?

The three measures of central tendency answer slightly different questions. Khan Academy (Statistics Education Platform) defines each precisely: median is the “middle value when ordered,” and mode is the “most frequent value.” Here’s how each one works.

Mean steps

Add all values, divide by the count. Example: data set {4, 6, 8, 10, 12, 14} → sum is 54, count is 6 → mean is 9.

Median steps

Order values from smallest to largest. If there’s an odd count, the median is the middle number. If even, take the average of the two middle numbers. For {4, 6, 8, 10, 12, 14}, the two middle values are 8 and 10, so median = (8 + 10) ÷ 2 = 9.

Mode steps

Find the value that appears most often. If every value appears the same number of times, there’s no mode. If multiple values share the highest frequency, you have multiple modes. MathsIsFun (Educational Math Site) notes that “the mode is the number which appears most often.”

What is the mean in math?

In mathematics, the mean is the arithmetic average — a measure of central tendency that represents the typical value in a dataset. The Khan Academy (Statistics Education Platform) explains it as “the ‘average’ number; found by adding all data points and dividing by the number of data points.”

Basic definition

The mean takes all values into account, unlike the median (which ignores extremes) or mode (which only counts frequency). It is calculated as the sum of all observed values divided by the number of observations.

When to use mean

The mean works best when your data is roughly symmetrical and free of extreme outliers. If one value skews heavily in either direction, the mean will shift toward that outlier, potentially giving a misleading picture. In those cases, the median often provides a more representative central value.

How to calculate mean in a frequency table?

Frequency tables organize data by grouping values with their frequencies — they make large datasets manageable but require a modified formula. For a discrete frequency table, YouTube: Mean Median Mode from Frequency Table Discrete explains that you multiply each value by its frequency, sum those products, then divide by the total frequency count.

Discrete frequency table formula

When values appear repeatedly, the mean formula becomes:

Mean = ∑(f × x) / ∑f

Here, f = frequency (how many times each value appears), x = the value itself, and ∑f = total count of all observations.

Example with a discrete table

Consider this frequency distribution:

Mean = 60 ÷ 10 = 6. This matches what you’d get listing out each value individually (five appears four times, six appears three times, and so on). If you’re interested in learning more about calculating the mean, you can find a helpful guide at Wie viele Beine hat eine Spinne.

Grouped frequency table (estimated mean)

When data is grouped into intervals, you can’t identify exact values — only estimates. MathsIsFun (Educational Math Site) states that “for grouped data, we cannot find the exact Mean, Median and Mode — we can only give estimates.”

For grouped data, use class midpoints:

1. Find the midpoint of each interval: (lower bound + upper bound) ÷ 2
2. Multiply each midpoint by its frequency
3. Sum those products and divide by total frequency

Using the grouped example from MathsIsFun (Educational Math Site) with runners’ heights: estimated mean = 61.333. The median and mode estimates from the same example are 61.4375 and 61.5 respectively — the three measures cluster closely, suggesting roughly symmetric grouped data.

“Mean: The ‘average’ number; found by adding all data points and dividing by the number of data points.”

— Khan Academy, Statistics Education Platform

“For grouped data, we cannot find the exact Mean, Median and Mode, we can only give estimates.”

— MathsIsFun, Educational Math Site

Summary

The mean is sum divided by count — a formula that works whether you’re calculating by hand or with a frequency table. Discrete tables let you find exact values; grouped intervals require midpoint estimation. Understanding when to use each approach, and when to prefer median over mean, is what separates routine calculation from genuine statistical judgment. For students, researchers, or anyone working with data: master these steps once, and you can apply them to any dataset you encounter.