# Calculate the average of a group of numbers

Suppose you want to find the average number of days to complete a milestone in a project or the average temperature on a particular day over a 10-year time span. There are several ways to calculate the average of a group of numbers.

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.
• 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.

What do you want to do?

## Calculate the average of numbers in a contiguous row or column

1. Click a cell below or to the right of the numbers for which you want to find the average.
2. On the Home tab, in the Editing group, click the arrow next to AutoSum , click Average, and then press ENTER.

## Calculate the average of numbers not in a contiguous row or column

To do this task, use the AVERAGE or the AVERAGEIF functions.

### Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
1. Press CTRL+C.
2. In the worksheet, select cell A1, and press CTRL+V.
3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
A
Data
10
7
9
27
0
4
Formula Description (Result)
=AVERAGE(A2:A7) Averages all of numbers in the range A2:A7 (9.5)
=AVERAGE(A2:A4,A7) Averages the numbers in cells A2, A3, A4, and A7 (7.5)
=AVERAGEIF(A2:A7, "<>0") Averages the numbers in the range A2:A7 except those that contain zero, such as cell A6 (11.4)

### Function details

AVERAGE    This function requires one or more arguments, which can be numbers, cell references, ranges, or defined names, up to a maximum of 255 arguments. For example, the formula AVERAGE(A2,A3,10,MyRange) returns the value 120, where A2=100, A3=500, and the defined name "MyRange" contains 10 cells that add up to 950.

AVERAGEIF     This function returns the average (arithmetic mean) of all the cells in a range that meet a given criteria. For example, the formula AVERAGEIF(H1:H10,">100") returns the average of only the numbers in the range H1:H10 that are greater than 100. If only four of the cells meet that criterion, only those four cells are averaged.

## Calculate a weighted average

To do this task, use the SUMPRODUCT and the SUM functions.

### Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
1. Press CTRL+C.
2. In the worksheet, select cell A1, and press CTRL+V.
3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.

This example calculates the average price paid for a unit across three purchases, where each purchase is for a different number of units at a different price per unit.

A B
Price per unit Number of units
20 500
25 750
35 200
Formula Description (Result)
=SUMPRODUCT(A2:A4,B2:B4)/SUM(B2:B4) Divides the total cost of all three orders by the total number of units ordered (24.66)

### Function details

SUM    This function adds all the numbers that you specify as arguments. Each argument can be a range, a cell reference, an array, a constant, a defined name, a formula, or the result from another function.

SUMPRODUCT    This function multiplies corresponding components in the given arrays, and returns the sum of those products.

## Calculate the average of numbers, ignoring zero (0) values

To do this task, use the AVERAGEIF function.

### Example

The example may be easier to understand if you copy it to a blank worksheet.

1. Create a blank workbook or worksheet.
2. Select the example in the Help topic.

Note   Do not select the row or column headers.

Selecting an example from Help
1. Press CTRL+C.
2. In the worksheet, select cell A1, and press CTRL+V.
3. To switch between viewing the results and viewing the formulas that return the results, press CTRL+` (grave accent), or on the Formulas tab, in the Formula Auditing group, click the Show Formulas button.
A
Data
10
7
9
27
0
4
Formula Description (Result)
=AVERAGEIF(A2:A7, "<>0") Averages the numbers in the range A2:A7 except those that contain zero, such as cell A6 (11.4)

Applies to:
Excel 2010