# Calculate the average of numbers

Let's say 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. Click the arrow next to AutoSum on the Standard toolbar (toolbar: A bar with buttons and options that you use to carry out commands. To display a toolbar, press ALT and then SHIFT+F10.), and then click Average and press ENTER.

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

To do this task, use the AVERAGE 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 Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.
A
Data
10
7
9
27
0
4
Formula Description (Result)
=AVERAGE(A2:A7) Averages all of numbers in list above (9.5)
=AVERAGE(A2:A4,A7) Averages the top three and the last number in the list (7.5)
=AVERAGE(IF(A2:A7<>0, A2:A7,"")) Averages the numbers in the list except those that contain zero, such as cell A6 (11.4)

Note    The last formula in the example must be entered as an array formula (array formula: A formula that performs multiple calculations on one or more sets of values, and then returns either a single result or multiple results. Array formulas are enclosed between braces { } and are entered by pressing CTRL+SHIFT+ENTER.). After copying the example to a blank worksheet, select the cell A11. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the error #VALUE! is returned.

AVERAGE

# Calculate a weighted average

To do this task, use the SUMPRODUCT and 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 Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.

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)

SUM

SUMPRODUCT

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

To do this task, use the AVERAGE and IF 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 Tools menu, point to Formula Auditing, and then click Formula Auditing Mode.
A
Data
10
7
9
27
0
4
Formula Description (Result)
=AVERAGE(IF(A2:A7<>0, A2:A7,"")) Averages the numbers in the list except those that contain zero, such as cell A6 (11.4)

Note    The formula in the example must be entered as an array formula (array formula: A formula that performs multiple calculations on one or more sets of values, and then returns either a single result or multiple results. Array formulas are enclosed between braces { } and are entered by pressing CTRL+SHIFT+ENTER.). After copying the example to a blank worksheet, select the cell A9. Press F2, and then press CTRL+SHIFT+ENTER. If the formula is not entered as an array formula, the error #VALUE! is returned.

AVERAGE

IF

Applies to:
Excel 2003