For example you want to calculate the average of Range A1:A10 from Sheet 1 to Sheet 5, you can easily solve it as follows:

Step 1: Select a blank cell, says Cell C3, enter the formula =AVERAGE(Sheet1:Sheet5!A1:A10) into it, and press the Enter key. Now you will get the average in the Cell.

Notes:
(1) In the formula of =AVERAGE(Sheet1:Sheet5!A1:A10), Sheet1:Sheet5 is the multiple adjacent sheets you will calculate the average from, and A1:A10 means the same cells/range you will calculate the average in the multiple sheets. You can change them based on your needs.
(2) If you want to calculate the average of different cells/range from different worksheets in Excel, for example you want to calculate the average of Range A1:A5 in Sheet1, Range A3:A6 in Sheet2, Range A7:A9 in Sheet3, Range A2:A10 in Sheet4, and Range A4:A7 in Sheet5, you should apply this formula =AVERAGE(A1:A5,Sheet2!A3:A6,Sheet3!A7:A9,Sheet4!A2:A10,Sheet5!A4:A7).

Kutools for Excel's Dynamically Refer to Worksheets utility can help users to extract values from the same cells of other worksheets. Therefore, we can take advanced of this utility to average same cells from multiple worksheets easily in Excel.

1. Create a new worksheet, and then select the cell that you will average from multiple worksheets. In our case, we select the Cell D7.

2. Click Kutools > More (in the Formula group) > Dynamically Refer to Worksheets.

3. In the opening dialog box, please (1) Specify a fill order from the Fill order drop down list. In our case, we select the Fill vertically cell after cell; (2) Go to the Worksheet list box, and check the worksheets whose cells you will average; (3) Click the Fill Range button, and close the dialog box. See screenshot:

4. Now the values are extracted from the certain cell of specified worksheet and fill into the new worksheet. Just select a blank cell, and apply the formula =AVERAGE(D7:D11) (D7:D11 is the range filled with extracted vales from other worksheets) and press the Enter key.

Sometimes, you many need to average same cells across multiple worksheets at the same time. For example, average Cell A1 from all worksheet, average Cell B1 from all worksheets, and so does Cell C1 simultaneously. You can try Kutools for Excel's Combine (worksheets and workbooks) utility to get it done easily!

1. Click Kutools Plus > Combine to open the Combine Worksheets wizard.

2. In the Combine Worksheets – Step 1 of 3 wizard, check the Consolidate and calculate values across multiple workbooks into one worksheet option, and click the Next button.

3. In the Combine Worksheets – Step 2 of 3 wizard, please:
(1) Check the worksheets you will average from in the Worksheet list;
(2) Click the Browse button  to select the range you will average;
(3) Click the Same Range button.
(4) Click the Next button.

4. In the Combine Worksheets – Step 3 of 3 wizard, please select Average from the Function drop down lit, specify labels based on your need, and click the Finish button.

5. A dialog box will pops out and asks you for saving the combination scenario. Click the Yes button or No button based on your needs. In our case, we click the No button.

So far the each cell in the specified range has been averaged from the specified worksheet.