Documentation/Calc Functions/MEDIAN
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Function name:
MEDIAN
Category:
Statistical Analysis
Summary:
Calculates the median of a set of unsorted data points. The median is the value in the middle of an ordered dataset and it separates the lowest 50% of values from the highest 50%.
After a set of numbers is arranged in ascending order:
- If the number of values is odd, the number in the middle of the set is the median.
- If the number of values is even, then the median is the simple average of the middle two numbers.
Syntax:
MEDIAN(Number 1 [; Number 2 [; … [; Number 255]]])
Returns:
Returns a real number, which is the median of the supplied data points.
Arguments:
Number 1, Number 2, … , Number 255 give the set of real numbers from which the median is to be calculated. Each argument may be a value or an expression, a reference to a single cell, a reference to a cell range, the name of a named or database range, or an inline array.
Note that although MEDIAN can accept up to 255 arguments, each argument could specify a range of cells. This means that the number of real numbers processed could be many more than 255.
The following conditions (including errors) may be encountered:
- If any argument is a string in quotation marks, then MEDIAN reports a parameter list error (Err:504).
- Text in cells and empty cells are ignored.
- If there are no supplied numbers, then MEDIAN reports a #VALUE! error.
- If only one value is supplied, then MEDIAN returns that value.
Additional details:
- If the number of values (n) in the ordered data set is odd, then the median is given by:
- [math]\displaystyle{ median(Y)\:=\:Y\left[\frac{n}{2}\right] }[/math]
- where Y represents the ordered data set.
- If the number of values in the ordered data set is even, then the median is given by:
- [math]\displaystyle{ median(Y)\:=\:\frac{ Y\left[ \frac{n-1}{2}\right] + Y\left[ \frac{n+1}{2}\right] }{2} }[/math]
- For more information on the median value, visit Wikipedia's Median page.
Examples:
| Formula | Description | Returns |
|---|---|---|
| =MEDIAN(A1:A5) where cells A1:A5 contain the values 5, 1, 9, 21, and 20 respectively. | For an odd number of values, the median will be the number in the middle of the set, when placed in ascending order. | 9 |
| =MEDIAN(5.5; 20; 9.5; 1.3) | For an even number of values, the median will be the average of the two values in the middle of the set. | 7.5 |
| =MEDIAN({5, 2, 8, 10, -2}) | For an odd number of values, the median will be the number in the middle of the set. | 5 |
Related LibreOffice functions:
ODF standard:
Related (or similar) Excel functions:
MEDIAN