Paste a comma-separated list of numbers to get the arithmetic mean, median, mode, range, and geometric mean, plus the largest and smallest values, the sum, the count, and the sorted data set.
Examples
Default list 10, 2, 38, 23, 38, 23, 21
The sum is 155 and n is 7, so the mean is 22.142857142857. Sorted, the middle value is 23 (the median). Largest 38 minus smallest 2 is a range of 36. Both 38 and 23 appear twice, so the mode is 38, 23, each appeared 2 times (first-appearance order). The geometric mean is 16.412764443111.
All unique values 1, 2, 3, 4
The mean and median are both 2.5, the range is 3, and the mode is All values appeared just once. The geometric mean is 2.2133638394006.
Negatives and zeros
For -2, 10, 0, 10, -2 the mean is 3.2, the median is 0, and the range
is 12. The mode is -2, 10, each appeared 2 times. Because the list
includes zero and negatives, the geometric mean is 0.
Formula
The mean is the sum of the n values divided by n:
mean = (x1 + x2 + … + xn) / n
Sort the list in ascending order to find the median. For an odd count the median is the middle value; for an even count it is the average of the two middle values.
range = largest − smallest
The mode is the value (or values) with the highest frequency. Geometric mean is the n-th root of the product:
gmean = (x1 × x2 × … × xn)^(1/n)
If any xi is zero or negative, geometric mean is reported as 0.
Mean, median, mode, and range each describe a different aspect of the same list. An outlier pulls the mean and the range far more than the median, so looking at all four together is more informative than any one figure alone.
Choosing a summary
Mean, median, mode, and range describe different features of the same list. The mean is sensitive to outliers, the median ignores distances between most observations, the mode may be absent or nonunique, and the range depends only on two values. Preserve units and the sampling context when comparing datasets.
Paste-ready data activity: the outlier changes the story
This original activity uses ten fictional wait times, measured in minutes. Paste the following line into the calculator:
6, 7, 7, 8, 8, 8, 9, 10, 12, 25
Before calculating, ask which single number looks unusual and predict whether the mean or median will be larger. Then use the sorted-data output to check the position of the middle values.
Student prompts
- Find the mean, median, mode, and range, and include minutes with every answer where the unit applies.
- Which measure of center better describes a typical wait for this data set? Support the choice with two calculated values.
- Remove the 25-minute observation and recalculate. Which summaries change?
- Could the 25 be a data-entry error? What information would you need before deleting it from a real data set?
- Write a different ten-value data set with the same median of 8 but no mode.
Answer check
For all ten waits, the sum is 100, so the mean is 10 minutes. The two
middle observations are both 8, making the median 8 minutes. The mode is
8 minutes, and the range is 25 − 6 = 19 minutes.
After removing 25, the sum is 75 across nine observations: the mean is about 8.333 minutes, the median is 8 minutes, the mode remains 8 minutes, and the range becomes 6 minutes. The original median and mode do not change, while the mean and range do. That contrast supports using the median when the goal is to describe the center without letting one long wait dominate—but the choice should still be explained in context.
An unusual observation is not automatically an error. In real work, check how the value was recorded and what happened during that observation before excluding it. The calculator summarizes the values supplied; it cannot judge their provenance or decide which statistic answers the research question.