Mean, Median, Mode, Range Calculator: Measures of Central Tendency & Dispersion
Free mean median mode range calculator: find the average of a data set, median for even or odd n, mode for bimodal data, and range. Step-by-step Logic Trace shows sorting, summation, frequency map, and how range is found.
What This Calculator Does
Purpose & who itโs for
- FeaturesFlexible input (comma, space, or newline separated). Random sample, Load example (test scores, heights), Clear. Adjustable mean precision (0โ5 decimals). Result pane with all nine statistics (including geometric mean, sum, count); sorted bar with Min, Max, and median highlighted; Copy to clipboard.
This mean median mode range calculator computes the four core statistics from a single data set: Mean (xฬ, arithmetic average), Median (xฬ, middle value), Mode (Mo, most frequent value(s)), and Range (R, max โ min). The Logic Trace shows sorting, the mean formula (ฮฃx / n), a frequency map for mode, and the range calculationโso you get both quick answers and a clear view of how each number is found. Itโs built for students checking homework, teachers explaining descriptive statistics, and anyone who needs to find the range of a data set, find mean with decimals, or calculate the median for an even number of values (average of the two middle values). Bimodal or multimodal data are supported: every value that ties for highest frequency is listed as a mode.
Measures of Central Tendency: Mean, Median, Mode
These three describe where the โcenterโ of the data lies, in different senses.
Mean (xฬ): The arithmetic average.
Median (xฬ): The middle value when the data is sorted. If n is odd, itโs the single center value; if n is even, itโs the average of the two middle values (so calculating the median for an even number of values is straightforward: sort, then average the two middle numbers). The median is resistant to outliers and is often preferred for incomes, house prices, or any data where extremes can distort the average.
Mode (Mo): The value or values that appear most often. A set can be unimodal (one mode), bimodal (two values tie for highest frequency), or multimodal. If no value repeats, there is no mode. This calculator lists every value that has the maximum frequency.
Mean (xฬ): The arithmetic average.
xฬ = (ฮฃxi) / n
Sum all values and divide by the count. The mean is sensitive to outliers: one very high or low value can pull it away from the rest. Use it when you want the balance point of the numbers.Median (xฬ): The middle value when the data is sorted. If n is odd, itโs the single center value; if n is even, itโs the average of the two middle values (so calculating the median for an even number of values is straightforward: sort, then average the two middle numbers). The median is resistant to outliers and is often preferred for incomes, house prices, or any data where extremes can distort the average.
Mode (Mo): The value or values that appear most often. A set can be unimodal (one mode), bimodal (two values tie for highest frequency), or multimodal. If no value repeats, there is no mode. This calculator lists every value that has the maximum frequency.
Measure of Dispersion: Range
Range (R) measures how spread out the data is:
R = Max โ Min
. You subtract the smallest value from the largest. Itโs easy to compute and interpret, but it uses only two values, so one extreme can make the range large. To find the range of a data set, sort the values (or scan for min and max), then subtract. This calculator shows the sorted list and highlights Min and Max so you can see exactly how the range is found.How to Calculate the Average of a Data Set Manually
To find the mean by hand: (1) Add all numbersโincluding decimalsโto get ฮฃx. (2) Count how many there are: n. (3) Divide:
xฬ = ฮฃx / n
You can round the result to a chosen number of decimal places. This toolโs Logic Trace shows the full sum and the division step so you can verify the result or follow along when learning how to find mean with decimals.Mean Median Mode Range Calculator FAQ
? What are mean, median, mode, and range?
Mean (xฬ) is the arithmetic average: sum of all values divided by how many there are. Median (xฬ) is the middle value when the data is sorted (or the average of the two middle values if there is an even number). Mode is the value or values that appear most often; a set can have one mode, two (bimodal), or more. Range is the spread: largest value minus smallest. This calculator finds all four and shows the steps in the Logic Trace.
? What is the difference between mean and median?
The mean (xฬ) is the arithmetic average: sum of all values divided by the count. The median (xฬ) is the middle value when the data is sorted. The median is better for data with outliers (e.g. incomes, house prices) because it isn't pulled by extremes. This mean median mode range calculator shows both and explains the steps in the Logic Trace.
? What if there are two modes?
A dataset can be bimodal (two values tie for highest frequency) or multimodal (more than two). This calculator lists all values that have the maximum frequency as the Mode. If no value repeats, it displays "No Mode."
? Is the mean or median better for outliers?
The median is more robust to outliers. One very large or very small value can shift the mean a lot but only slightly affects the median (or not at all in small sets). Use the median when you want a "typical" value that isn't distorted by extremes.
? How do I find the range of a data set?
The range is
R = Max โ Min
: subtract the smallest value from the largest. It measures spread. This tool sorts your data and shows Min and Max in the Logic Trace and in the sorted bar (highlighted in green and red) so you can see exactly how range is computed.? How to find mean with decimals?
Add all values (including decimals), then divide by the count:
xฬ = ฮฃx / n
For example, the mean of 10.5, 20.25, and 30.1 is (10.5 + 20.25 + 30.1) รท 3 = 20.28โฆ This calculator supports decimals and lets you set mean precision (0โ5 decimal places) for the result.? How do you calculate the median for an even number of values?
When n is even, the median is the average of the two middle values after sorting:
median = (middleโ + middleโ) / 2
For example, for 2, 4, 6, 8 the middle values are 4 and 6, so median = (4 + 6) / 2 = 5. The Logic Trace shows the sorted list and which positions are used for the median.