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Average Calculator

Calculate mean, median, mode, and weighted mean with clear step-by-step math.

Enter dataset

Use commas, spaces, line breaks, or semicolons as separators.

Results

Primary result: Arithmetic Mean

21.666667

Count

6

Sum

130

Min

10

Max

30

Range

20

Mean

21.666667

Median

22.5

Mode

30

Step-by-Step Calculation

1. Dataset

x={10, 20, 30, 15, 25, 30}x = \{10,\ 20,\ 30,\ 15,\ 25,\ 30\}

2. Sorted dataset

xsorted={10, 15, 20, 25, 30, 30}x_{sorted} = \{10,\ 15,\ 20,\ 25,\ 30,\ 30\}

3. Mean

xˉ=∑xiN=1306=21.666667\bar{x} = \frac{\sum x_i}{N} = \frac{130}{6} = 21.666667

4. Median

Median=x3+x42=20+252=22.5\text{Median} = \frac{x_{3} + x_{4}}{2} = \frac{20 + 25}{2} = 22.5

5. Mode

10:110: 1
15:115: 1
20:120: 1
25:125: 1
30:230: 2
Mode=30\text{Mode} = 30

Value Frequency

What is an average?

In everyday language, "average" usually means one number that summarizes a dataset. In statistics, there are several common measures of central tendency:

  • Arithmetic mean: Add all values and divide by the count.
  • Median: The middle value after sorting the dataset.
  • Mode: The most frequent value(s).

Each measure can be the best choice depending on your data.

Mean, median, and outliers

The arithmetic mean uses every value equally, which makes it useful but also sensitive to outliers. A single extreme value can pull the mean up or down.

The median is more robust because it depends on position, not magnitude. If your data contains extreme values (for example, income data), the median often gives a better sense of the typical value.

Understanding mode

The mode is the most frequent value in a dataset.

  • If one value appears most often, the dataset is unimodal.
  • If multiple values tie for highest frequency, it is multimodal.
  • If all values occur once, there is no mode.

Mode is especially useful for categorical or discrete data, such as the most common shoe size, favorite color, or most selected answer option.

Weighted average

A weighted average assigns different importance to each value. Instead of treating every value equally, each value is multiplied by its weight.

The formula is:

xˉw=∑wixi∑wi\bar{x}_w = \frac{\sum w_i x_i}{\sum w_i}

Common use cases include:

  • GPA (courses with different credit hours)
  • Portfolio returns (assets with different allocations)
  • Course grade weighting (exams, homework, projects with different percentages)

How to use this calculator

  1. Enter your dataset in the values box (comma, space, or newline separated).
  2. Choose Basic for mean/median/mode, or Weighted to also compute weighted mean.
  3. If using Weighted mode, enter one zero-or-positive weight per value.
  4. Click Calculate.
  5. Review summary stats and the step-by-step formulas to understand how each result was derived.

Do not use grouped-number formatting such as 1,000; enter 1000 instead.

Interpreting results

  • Use mean for balanced numeric datasets without extreme outliers.
  • Use median when outliers may distort the mean.
  • Use mode to identify most common values.
  • Use weighted mean when observations should contribute unequally.

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