This mean median mode calculator summarizes a numerical dataset or an exact frequency table, including all tied repeated modes and the range.
Choose a mean, median or mode to describe the data
The mean adds every observation and divides by the observation count. The median locates the middle of the ordered data. The mode identifies the most frequent observed value. These describe different aspects of the same dataset, so a single average can hide information. OpenStax explains the three measures of center; the official Python statistics documentation defines the corresponding arithmetic and numerical order-statistic operations. Mean and median retain the original measurement unit. A large value can move the mean substantially while leaving the middle positions unchanged. That does not make the value invalid. This calculator keeps every valid observation instead of deleting outliers automatically. This calculator uses a repeated-value convention. It returns every value tied for the highest frequency when that frequency exceeds one. If every observed value appears once, it reports no repeated-value mode. Other conventions are possible: Python’s multimode function returns all equally frequent values, including an all-distinct dataset. The result label makes this page’s convention explicit.
Use observations of the same quantity in the same unit. Convert mixed units first.
An extreme value stays in the dataset. Compare mean and median before interpreting the center.
Check a dataset with two modes
Enter 1, 1, 2, 5, 6, 6, 9. The engine counts 7 observations and sums them to 30. Dividing the sum by the count gives mean 4.285714286.
The ordered list is already in ascending order. Its middle value is 5, so that is the median. Values 1 and 6 each appear 2 times, making both repeated modes. Returning only one would discard a tie.
The minimum is 1 and maximum 9. Their difference gives range 8. Range measures the distance between the extremes, rather than the center or the spread around the mean. Open Calculation details to check the sum, middle positions and ordered frequencies.
Read frequencies and an ordered median
Paste individual observations separated by commas, spaces, tabs, semicolons or new lines. Decimals, scientific notation and simple fractions are accepted. Omit thousands separators: a comma separates observations and would split one large number.
For a frequency table, enter one exact value and its nonnegative whole-number count per line. These counts represent repeated observations, rather than reliability weights. Duplicate numerical values combine. A zero-count row contributes no observation.
The frequency preset enters 5 with count 3, 6 with count 1, and 7 with count 2. It represents 6 observations with sum 35 and mean 5.833333333. The median uses ordered observation positions, not the number of table rows. The two central values are 5 and 6. Their average gives median 5.5. The repeated mode is 5, with frequency 3.
Class intervals do not preserve the individual values needed for exact medians and modes. This page accepts exact value/count pairs rather than interpolating an unknown center from class bounds. Arbitrary nonnegative relative weights belong in the separate weighted-average job.
Handle ties, outliers and finite-precision inputs
All tied repeated modes are returned. A singleton or an all-distinct list has no repeated-value mode under the convention declared above. The fraction preset has mean 1, median 1 and range 3, with no repeated mode. Different textual forms of the same represented number share a frequency.
The Standard Deviation Calculator measures spread around the mean and distinguishes sample and complete-population conventions. The Interquartile Range Calculator measures the middle-half spread using a named quartile method. Values beyond its fences are not silently removed here. Use Ratio when the task is to simplify proportional terms rather than summarize observations.
Local capacity limits are 5,000 observations or rows, 100,000 characters in the selected field, and 1,000,000,000 total observations in an exact frequency table. A numerical token supports at most 128 characters. Nonzero input magnitudes must be from 1e-100 to 1e+100. These are implementation limits rather than statistical thresholds.
Calculations use IEEE754 floating-point values and compensated sums. Fractions may be approximate, and differences below machine precision cannot be recovered. Median and mode ordering use the represented numerical values; the display rounds only after calculation. Details show the first 100 unique-value rows, while every accepted observation contributes to the result. Large frequency totals are processed as counts without expanding them into a billion-element list.
When two distinct values would receive the same rounded label, mode and ordered-value labels keep enough digits to distinguish them. This display exception preserves value identity; it does not create extra input precision.
Use the Weighted Average Calculator to combine values with nonnegative relative weights and inspect their normalized contributions. It computes a generic mathematical average rather than a course-specific grading policy.
Once you have a reference mean and positive standard deviation, the Z-Score Calculator measures a value's signed distance in standard deviations. Normal areas require a separate, explicit normal-model assumption.
When the measurement has a meaningful zero, the Coefficient of Variation Calculator compares SD to a nonzero mean. It distinguishes signed CV from absolute percentage RSD and warns when the measurement scale makes relative interpretation inappropriate.
The Pooled Standard Deviation Calculator combines sample spreads with degrees-of-freedom weights. Keep groups separate; its within-group result differs from the standard deviation of all observations together.
The Mean Absolute Deviation Calculator averages absolute distances from the mean and offers a clearly labeled unscaled median absolute deviation. Its distance aggregation differs from squared-deviation SD.
The Geometric Mean Calculator averages multiplicative values or equal-period factors. It separates raw values, relative weights and percentage changes, with explicit zero conventions.
The Harmonic Mean Calculator averages positive values through their reciprocals. For speeds, it separates equal-distance averaging from equal-time arithmetic averaging and accepts relative distance weights.