How an equal-weight mean summarizes a list of numbers
The arithmetic mean divides the sum of equally weighted observations by their count. The median and range provide context because a single extreme number can move the mean away from a typical observation.
The arithmetic mean gives each entered observation one equal vote, including duplicate values. The tool also sorts the list to find the median: the central item for an odd count or the average of two central items for an even count. Looking at both measures helps spot a mean influenced by a large outlier.
The tool shows sum, count, mean, median and values distributed around the mean. This makes an equal-weight average checkable and flags when a lone extreme value may pull it away from the middle.
How the number list, separators and outliers move the mean
The only input is the list itself, so the result depends on how the text is split into numbers and on which numbers are in it.
- Numbers list
- Every value you paste becomes one observation with equal weight, up to 100 values. Negative numbers, decimals and scientific notation are accepted, so 1e3 and −2.5 average to 498.75. Text such as a percent sign or a unit is rejected rather than skipped: entering 5% stops the calculation with an invalid-number message.
- Separators
- Commas, spaces and line breaks all split values, so a comma is never read as a thousands separator. Typing 1,000, 2,000 produces four values, 1, 0, 2 and 0, and a mean of 0.75 instead of 1,500. Remove digit-grouping commas before pasting figures copied from a spreadsheet or report.
- Outliers
- One extreme value can drag the mean far from the rest while barely moving the median. The list 10, 11, 12, 13 and 100 has a mean of 29.2 and a median of 12, and four of the five values sit below the mean. When the two measures disagree that much, confirm the large value belongs in the list.
- Six-decimal display
- The mean, sum and median are printed to at most six decimal places, so 1, 2 and 2 give a mean of 1.666667. The below, equal and above counts compare each value with the unrounded mean, so a value that looks identical to the printed mean can still be counted on one side of it.
Steps
- Enter up to 100 finite numbers, separated by commas, spaces or line breaks.
- Run the calculator to see their sum and count.
- Compare the mean with the sorted middle value and inspect how many observations fall above or below the mean.
Reading tip: Enter a list, not a precomputed total. A repeated number is counted again. The below/at/above groups classify raw observations against the unrounded mean.
Lists where a simple equal-weight mean is the right summary
Summarize measurements
Compute a mean from repeated observations with equal weight.
Compare mean and median
Check whether a skewed list pulls the average away from the central observation.
Verify a total
See the exact count and sum behind the headline mean.
Inspect spread
Use the minimum, maximum and above/below groups for quick context.
How the calculation works
- xᵢ
- Each entered finite number, counted again if it occurs more than once.
- S
- Sum of every parsed observation before rounding for display.
- n
- Count of observations, from one through one hundred.
- median
- Middle of the sorted values, shown separately from the equal-weight mean.
This is an equally weighted arithmetic mean. The median is contextual information, not an alternative input weighting.
What every part means
- xᵢ
- Each entered finite number, counted again if it occurs more than once.
- S
- Sum of every parsed observation before rounding for display.
- n
- Count of observations, from one through one hundred.
- median
- Middle of the sorted values, shown separately from the equal-weight mean.
Calculate it step by step
Add every entered finite number, including zero and negatives.
Divide the sum by the observation count, not by a fixed interval width.
Sort a copy of the list; the median is a separate measure from the mean.
Inputs are parsed at Decimal precision. The headline is rounded to six decimals; classifications and median use unrounded values.
See how Calculation Guide tests examples and handles calculation limits.
See it in practice
- Numbers
- 10, 20, 30
Values 10, 20 and 30: S = 10 + 20 + 30 = 60; n = 3; mean = 60/3 = 20. Sorted middle value and median are also 20.
- Count3
- Sum60
Interpretation & limitations
How to read your result
The mean is useful when every observation has equal importance. If mean and median differ sharply, inspect the range and the original values before treating either as typical.
Where this estimate stops
This is not a weighted mean and does not infer missing values or remove outliers. The parser accepts at most 100 comma-, space- or newline-separated numbers.
Frequently asked questions
01Is this a weighted average?
No. Every entered observation contributes equally, including repeated values.
02Can negative and decimal numbers be used?
Yes. The mean and median preserve their values; the output is rounded for display.
03Do duplicates count once or twice?
Each occurrence counts as its own observation in both the sum and count.
04What if there is only one number?
Its mean, median, minimum and maximum all equal that number.
05How is median computed for an even count?
The two middle sorted values are added and divided by two.
06Why may the mean not be one of the entered numbers?
A sum divided by the count can fall between observations, especially when values are spread out.