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

Associated Learning Objectives: 

• 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

Step-by-Step Instruction:

To calculate the mean:

1. 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.
2. Enter “=A2*B2” in cell C2.
3. Use the fill down feature to extend the formula from C2 down to calculate products for all rows of the distribution.
4. 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).

To calculate the standard deviation of a discrete random variable:

1. Follow the steps for the mean.
2. Enter “=((A2-C$#)^2)*B2” in cell D2, where # is the row number of the mean calculated in step 4.
3. Use the fill down feature to extend the formula from D2 down to the final row of the distribution.
4. 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))”.