AVERAGE function

AVERAGE function



This article describes the formula syntax and usage of the AVERAGE function in Microsoft Excel.



Description Returns the average (arithmetic mean) of the arguments. For example, if the range A1:A20 contains numbers, the formula =AVERAGE(A1:A20) returns the average of those numbers.



Syntax AVERAGE(number1, [number2], ...) The AVERAGE function syntax has the following arguments:

• Number1 Required. The first number, cell reference, or range for which you want the average.
  
  Number2, ... Optional. Additional numbers, cell references or ranges for which you want the average, up to a maximum of 255.

Remarks

• Arguments can either be numbers or names, ranges, or cell references that contain numbers.
• Logical values and text representations of numbers that you type directly into the list of arguments are counted.
• If a range or cell reference argument contains text, logical values, or empty cells, those values are ignored; however, cells with the value zero are included.
• Arguments that are error values or text that cannot be translated into numbers cause errors.

If you want to include logical values and text representations of numbers in a reference as part of the calculation, use the AVERAGEA function.



If you want to calculate the average of only the values that meet certain criteria, use the AVERAGEIF function or the AVERAGEIFS function.



Note: The AVERAGE function measures central tendency, which is the location of the center of a group of numbers in a statistical distribution. The three most common measures of central tendency are:

• Average, which is the arithmetic mean, and is calculated by adding a group of numbers and then dividing by the count of those numbers. For example, the average of 2, 3, 3, 5, 7, and 10 is 30 divided by 6, which is 5.
  
  
  
  
  
  
  
  The mathematical Mean is the same as the Average function. The formula is
  
  
  
  
  
  
  
  Where :
  
  x?? - Mean or Average of the numbers.
  
  n - is the sample size of Number of elements.
  
  x - The value of each element or number in the data set.
  
  
  
  To find the mean(average) of 5 numbers this would expand as below:
  
  
  
  
• Median, which is the middle number of a group of numbers; that is, half the numbers have values that are greater than the median, and half the numbers have values that are less than the median. For example, the median of 2, 3, 3, 5, 7, and 10 is 4.
• Mode, which is the most frequently occurring number in a group of numbers. For example, the mode of 2, 3, 3, 5, 7, and 10 is 3.

For a symmetrical distribution of a group of numbers, these three measures of central tendency are all the same. For a skewed distribution of a group of numbers, they can be different. Tip: When you average cells, keep in mind the difference between empty cells and those containing the value zero, especially if you have cleared the Show a zero in cells that have a zero value check box in the Excel Options dialog box in the Excel desktop application. When this option is selected, empty cells are not counted, but zero values are.

To locate the Show a zero in cells that have a zero value check box:

• On the File tab, click Options, and then, in the Advanced category, look under Display options for this worksheet.

Example Copy the example data in the following table, and paste it in cell A1 of a new Excel worksheet. For formulas to show results, select them, press F2, and then press Enter. If you need to, you can adjust the column widths to see all the data.