Enter the raw observations once. The calculator sorts the list, counts frequencies, and keeps each definition visible beside its result.
Result
Mean 5, median 3, mode 3, range 8
xˉ=5,x=3,mode=3,R=8
Conditions
Every entry must be a finite real number measured on a comparable scale.
The median is found only after sorting the data.
All values tied for the greatest frequency are reported as modes.
When every value occurs equally often, this page reports no mode rather than listing every value.
Steps
Sort the observations The list is already in ascending order.2,3,3,7,10
Calculate the mean The values total 25, and there are five observations.xˉ=25/5=5
Locate the median and mode The third value is the median, and 3 has the highest frequency.x=3,mode=3
Find the range Subtract the minimum from the maximum.R=10−2=8
✓
Independent check
The ordered list has two values on either side of the median. The frequency table counts 3 twice and every other value once, while 5 times the count 5 recovers the sum 25.
Scope
What this mean, median, mode and range calculator covers
For 2, 3, 3, 7, and 10, the mean is 5, the median is 3, the mode is 3, and the range is 8. These measures answer different questions about the same data.
Mean and median
Compare the arithmetic balance point with the middle of the ordered observations.
Examples: 2, 3, 3, 7, 10, 1, 2, 3, 4, 20
One mode, several modes, or no mode
Build a frequency table and report every value tied for the highest nontrivial frequency.
Examples: 1, 1, 3, 1, 1, 2, 2, 5, 2, 4, 6
Even and odd list lengths
Use one middle value for odd counts and average the two middle values for even counts.
Examples: 1, 3, 9, 1, 3, 7, 9
Range and sorted output
Show the ordered observations, minimum, maximum, and maximum minus minimum.
Examples: R=x_{\max}-x_{\min}
How to use it
Enter enough information for one clear task
1
Enter the raw data
Use commas, spaces, or new lines and include each repeated observation separately.
2
Inspect the sorted list
Confirm that the parser kept signs, decimals, and duplicate values before reading position-based results.
3
Compare the measures
Use the mean for arithmetic balance, the median for ordered position, and the mode for the most frequent value or category.
4
Read the range cautiously
The range uses only the two endpoints, so it does not describe how values are distributed between them.
Worked inputs
Examples to try
Use these examples to recognize the method, compare equivalent forms, and check your own work.
One clear mode
Sort, total the values, and count each frequency.
2,3,3,7,10
Expected result
xˉ=5,x=3,mode=3,R=8
Two modes
Both 1 and 2 occur twice, which is the greatest frequency.
1,1,2,2,5
Expected result
xˉ=2.2,x=2,modes=1,2
No repeated value
Every value has the same frequency, so this page uses the no-mode convention.
2,4,6
Expected result
xˉ=4,x=4,no mode
Even number of observations
Average the two middle ordered values for the median.
1,3,7,9
Expected result
xˉ=5,x=23+7=5
Mean affected by an extreme value
Compare the arithmetic total with the unchanged middle position.
1,2,3,4,20
Expected result
xˉ=6,x=3
All observations equal
The shared value is the mean, median, and single mode; the range is zero.
5,5,5,5
Expected result
xˉ=x=mode=5,R=0
Complete example
Compare four summaries for a five-value data set
One input can support several summaries, but each summary follows a different definition and should be interpreted separately.
2,3,3,7,10
1
Order the values
Ordering establishes the median position and endpoints.
2≤3≤3≤7≤10
2
Find the arithmetic balance point
The total is 25 across five observations.
xˉ=25/5=5
3
Find the center by position and frequency
The third value is 3, and 3 is also the only value that repeats.
x=3,mode=3
4
Measure the endpoint span
The data extend from 2 through 10.
R=10−2=8
xˉ=5,x=3,mode=3,R=8
Verification: The reverse mean check gives 5 times 5 equals 25. The ordered list confirms the middle position and endpoints, and a direct frequency count confirms the mode.
Avoidable errors
Common mistakes and how to fix them
Finding the median before sorting
Problem: Taking the value typed in the visual middle of the input list.
Why it matters: Median depends on ordered position, not entry order.
Better approach: Sort first, then locate one middle value or average the two middle values.
Forcing exactly one mode
Problem: Selecting one value when several values share the greatest frequency.
Why it matters: A distribution can be bimodal or multimodal.
Better approach: Report every value tied for the greatest nontrivial frequency.
Confusing range with a center
Problem: Treating maximum minus minimum as a typical value.
Why it matters: Range measures endpoint spread and is not a location measure.
Better approach: Keep mean, median, mode, and range labels attached to their definitions.
Ignoring the data type
Problem: Trying to calculate a mean for nominal categories such as colors.
Why it matters: Arithmetic and ordered positions require numerical or meaningfully ordered values.
Better approach: Use the mode for nominal categories and reserve the mean for quantitative data.
Trust the result for the right reasons
Checks, assumptions, and limits
How results are checked
The ordered list is generated independently from the original entry order.
The mean is multiplied by the count to recover the original sum within numeric tolerance.
Median indices are checked against odd and even observation counts.
A complete frequency table determines all tied modes, and range is checked as maximum minus minimum.
When to stop and revise the input
This input accepts finite quantitative observations, not categorical labels or grouped frequency intervals.
The no-mode convention is stated because some software instead labels every equally frequent value as a mode.
Range depends only on the minimum and maximum and can change sharply with one extreme observation.
These summaries do not establish causation, sampling quality, or distribution shape by themselves.
Common questions
Compare center and range for one data set FAQ
What is the difference between mean, median, and mode?
The mean is the arithmetic balance point, the median is the middle of the ordered data, and the mode is the most frequent value or category.
Can a data set have more than one mode?
Yes. Every value tied for the greatest frequency is a mode. A set with two such values is bimodal.
What happens when there are two middle values?
For quantitative data with an even count, the median is the arithmetic mean of the two middle ordered values.
Why can the mean and median be far apart?
An extreme value changes the total used by the mean but may barely change the middle position used by the median. A large gap can be a clue that the distribution is skewed or contains outliers.
Sources and curriculum alignment
This page follows standard introductory mathematics notation and learning sequences. Use these references to continue with a complete course treatment.
