Find the Mean and Standard Deviation from a One-Way Table

# Find the Mean and Standard Deviation from a One-Way Table

How to Find the Mean and Standard Deviation from a One-Way Table in Google Sheets

Written by Michael Mancuso

Updated over a week ago

- Find the mean from a frequency table
- Find the mean of a discrete random variable from its probability density function
- Find the standard deviation of a discrete random variable from its probability density function

- Paste the frequency distribution (or probability distribution) into cell A1 of Google Sheets so the values are in column A and the frequencies are in column B.
- Enter “=A2*B2” in cell C2.
- Use the fill down feature to extend the formula from C2 down to calculate products for all rows of the distribution.
- In a blank cell in column C, enter “=SUM(C2:C#)/SUM(B2:B#)” (for a frequency distribution) or “=SUM(C2:C#)” (for a probability distribution) to calculate the mean of the distribution, where # is the row number of the final row in the distribution table. For example, if the table goes down to row 5, enter “=SUM(C2:C5)/SUM(B2:B5)” (for a frequency distribution) or “=SUM(C2:C5)” (for a probability distribution).

- Follow the steps for the mean.
- Enter “=((A2-C$#)^2)*B2” in cell D2, where # is the row number of the mean calculated in step 4.
- Use the fill down feature to extend the formula from D2 down to the final row of the distribution.
- In a blank cell, enter “=SQRT(SUM(D2:D#)/(SUM(B2:B#)-1))” to calculate the standard deviation of a probability distribution, where # is the row number of the final row in the distribution table. For example, if the table goes down to row 5, enter “=SQRT(SUM(D2:D5)/(SUM(B2:B5)-1))”.