Mean, middle value, and repeated values
The mean divides the sum by the count. The median uses the middle sorted value or the average of the two middle values. The mode lists every value tied for the highest repeated frequency. The frequency breakdown combines identical numeric values and sorts them in ascending order. It shows the first 100 distinct values; every observation still contributes to the mean, median, modes, sum, and range. The share column is the percentage of observations with that value.
To measure how widely the values vary around the mean, use the Standard Deviation Calculator with the same dataset.
For the chance of a specified number of successes in independent trials, the Probability Calculator provides a binomial model rather than a summary of observed values.
The formula
Median and mode describe the center differently from the mean. Sorting affects the median calculation but does not change the underlying dataset.
A five-value dataset
For 1, 2, 2, 4, 6, the sum is 15 and mean is 3. The sorted middle value is 2, the repeated mode is 2, and the range is 5.
How to use this calculator
- Choose individual numbers to paste observations, or values with frequencies to enter each number beside its positive whole count.
- Calculate to see mean, median, mode, count, sum, and range. Check that the count matches the number of observations you intended.
- Compare mean, median, and mode before choosing a representative center.
The mean can respond strongly to extremes
Every value contributes to the arithmetic mean, so one unusually high or low observation can move it substantially.
The median depends on position after sorting and can better describe a skewed distribution, though context determines which measure is useful.
A dataset may have several modes
If multiple values share the highest repeated frequency, each is reported as a mode.
When every value appears once, this calculator reports no repeated mode rather than declaring every observation a mode.
Entering repeated observations
Frequency mode expands each count into that many equal-weight observations. You can use editable rows or paste two spreadsheet columns. Up to 200 frequency rows are accepted, totaling at most 10,000 observations, with values within ±1,000,000,000,000. Duplicate value rows add together. Counts must be positive integers; percentages, fractional weights, and grouped class intervals are outside this mode.
The frequency breakdown combines identical numeric values and sorts them in ascending order. It shows the first 100 distinct values; every observation still contributes to the mean, median, modes, sum, and range. The share column is the percentage of observations with that value.
Assumptions & limitations
What this calculation assumes
- Each individual token or expanded frequency count represents one observation.
- All observations have equal weight.
- Mode comparison uses exact entered numeric values.
- Each frequency is an exact whole count of identical observations.
What to keep in mind
- The calculator accepts at most 10,000 values.
- Rounded measurements that look similar can remain distinct values.
- These summaries do not describe distribution shape or uncertainty.
- Commas separate observations, so 1,000 is read as two values, 1 and 0. Labels, percent symbols, and measurement units must be removed before entry.
- Frequency entry accepts up to 200 rows totaling 10,000 observations; it does not estimate data from class intervals.
Common questions
Is average the same as mean?
In common usage average often means arithmetic mean, though average can refer to other measures in some contexts.
How is median calculated for an even count?
The two middle sorted values are added and divided by two.
Can there be more than one mode?
Yes. Every value tied for the highest repeated count is listed.
Can I calculate an average with unequal weights?
Whole observation frequencies are supported by frequency mode. For fractional weights, quantities that are not observation counts, or course credits, use the weighted average calculator. Each expanded observation here receives equal weight.
Can I enter repeated values without typing every observation?
Yes. Choose values with frequencies and enter the exact number beside its positive whole count. A row 4, 3 has the same effect as entering 4 three times.
Sources & further reading
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