Average Calculator — Mean, Median, Mode and Range

The word “average” means different things in different situations. A teacher wants the mean of exam scores. A property analyst wants the median house price. A retailer wants the mode — the most common shoe size. This free average calculator finds all three simultaneously, along with the range, sum, count, minimum and maximum — with a full step-by-step solution for each.

Mean — The Arithmetic Average

The mean is the sum of all values divided by the count of values. It is what most people mean when they say “average.”
Formula: Mean = Sum ÷ Count
Example: 10, 25, 38, 42, 15 Sum = 130 · Count = 5 · Mean = 130 ÷ 5 = 26
Use the mean when: your data has no extreme outliers — test scores, temperatures, prices of similar items.
Avoid the mean when: one extreme value distorts the picture. At a company where the CEO earns £2 million and ten employees earn £25,000, the mean salary is £200,000 — a number that represents nobody.

Median — The Middle Value

The median is the middle value when numbers are sorted from smallest to largest. For an even count the median is the average of the two middle values.
Odd count example: 5, 10, 15, 20, 100 Sorted: 5, 10, 15, 20, 100 · Median = 15
Even count example: 5, 10, 20, 100 Middle two: 10 and 20 · Median = (10 + 20) ÷ 2 = 15
The mean of the odd example is 30 — pulled up by 100. The median stays at 15. This is why house prices and salaries are always reported as medians — a few extreme values would make the mean meaningless.
Use the median when: your data has outliers or is skewed — house prices, salaries, income data.

Mode — The Most Frequent Value

The mode is the value that appears most often. A data set can have no mode, one mode or multiple modes.

Example: 3, 5, 5, 7, 8, 9, 9, 9 → Mode = 9 (appears 3 times)
Bimodal example: 2, 2, 5, 5, 8 → Mode = 2 and 5 (both appear twice)

Use the mode when: you want the most common value — most popular shoe size, most frequent exam score, most common survey response.

Range — How Spread Out the Data Is

Formula: Range = Maximum − Minimum

Example: 10, 25, 38, 42, 15 → Range = 42 − 10 = 32

The range is used alongside the mean. Two classes both averaging 70% on an exam tell different stories if one has a range of 10 (everyone scored similarly) and the other has a range of 60 (scores varied wildly).

Use the Percentage to GPA tab in the GPA calculator to convert instantly. This is particularly useful when applying to US universities from countries that use percentage grading system.

When to Use Mean vs Median vs Mode

Situation	Best measure
Exam scores, temperatures	Mean
House prices, salaries, income	Median
Most popular size, colour, response	Mode
Data with extreme outliers	Median
Symmetric data — bell curve	Mean
Skewed data — long tail	Median

Real example: The mean US household income in 2023 was approximately $105,000. The median was approximately $74,500. The mean is pulled up by very high earners — the median gives a more accurate picture of what a typical American household actually earns.

How to Calculate a Weighted Average

When values do not all count equally a simple average gives the wrong answer. Multiply each value by its weight, add the weighted values together and divide by the total weight.

Example — student course grade:

Midterm exam: 65% — weight 30
Final exam: 78% — weight 50
Coursework: 90% — weight 20

Simple average = (65 + 78 + 90) ÷ 3 = 77.6% ❌

Weighted average = (65×30 + 78×50 + 90×20) ÷ (30+50+20) = 76.5% ✅

The final exam carries more weight so the result is pulled closer to 78% than to the coursework score of 90%. Use the Weighted Grade Average tab to calculate this automatically.

Other Free Tools

Percentage Calculator — Percentage of a number, change and markup
GPA Calculator — Grade point average on the US 4.0 scale
Word Counter — Words, characters, sentences and reading time
Random Number Generator — Pick random numbers, roll dice, flip a coin

Frequently Asked Questions

Add all the numbers together and divide by how many numbers there are. The average of 10, 20 and 30 is (10 + 20 + 30) ÷ 3 = 20. Paste your numbers into the average calculator above and click Calculate to get the mean, median, mode and range instantly with the full working shown.

In everyday use mean and average are the same thing — both refer to the arithmetic mean. In statistics “average” is a broader term covering mean, median and mode. When someone says “find the average” they almost always mean the arithmetic mean: add up all values and divide by the count.

The mean of the numbers 1 through 10 is 5.5. The sum of 1+2+3+4+5+6+7+8+9+10 = 55. Divided by 10 numbers = 5.5. The median is also 5.5 — the average of the two middle values 5 and 6.

If every number in the data set appears only once there is no mode. The average calculator displays “No mode” in this case. If two values tie for most frequent the set is bimodal and both values are shown as the mode.

Multiply each value by its weight, add the results together and divide by the total weight. The Weighted Grade Average tab in this average calculator does this automatically — enter your scores and weights and the result appears instantly with the step-by-step calculation shown.

The range is the difference between the maximum and minimum values in a data set — it measures how spread out the numbers are. A small range means values cluster together. A large range means they are scattered. The average calculator shows the range alongside the mean, median and mode automatically.

Yes — the average calculator accepts numbers separated by commas, spaces or new lines. Copy a column of numbers from Excel and paste directly into the input field. The calculator handles any combination of separators automatically.

The mean is the sum of all values divided by the count — it is affected by every value including extreme outliers. The median is the middle value when sorted — it is unaffected by outliers. For symmetric data they give similar results. For skewed data such as incomes or house prices the median is more representative of the typical value.

About This Average Calculator

This average calculator is part of CalcDaysTime — a free suite of date, time and maths tools. All calculations run entirely in your browser. No data is sent to our servers, stored or shared with anyone.

Disclaimer: Results are calculated from the numbers you enter. Always verify statistical calculations against your institution’s official records before using in academic submissions or reports.