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Calculating the Variance and Standard Deviation Using Microsoft Excel Audio In this Microsoft Excel tutorial we will review how to calculate variance and standard deviation. Variance and standard deviation are widely used measures of dispersion. We will demonstrate how to calculate these measures two ways. First, we will calculate these measures as if Excel were merely a simple handheld calculator. Second, we will use Excel’s built-in functions. Video The video displays the title page. Edward Volchok, PhD Page 1 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Variance and standard deviation are closely related measures of dispersion. Video The video displays the words, “Variance and Standard Deviation are closely related.” Edward Volchok, PhD Page 2 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Both measure the deviation of variables from the mean. And, because they required the mean, you must use interval or ratio level data to calculate these measures. Video The video displays the words, “Both measure the spread of variables from the mean.” Edward Volchok, PhD Page 3 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The larger the variance or standard deviation indicated that the data are more variable. Video The video displays the words; “The larger the value the more variable the data.” Edward Volchok, PhD Page 4 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio A smaller variance or standard indicates that the data are less variable or more consistent. The smallest variance and standard deviation possible is zero. A variance or standard deviation of zero indicates that all random variables are the same. Video The video displays the words; “The smaller the value the less variable the data.” Edward Volchok, PhD Page 5 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Population variance is the mean of the sum of the squares of the random variables minus the population mean, mu, divided by the number of observations, or N. The formula of the population variance, or sigma squared, is the sum of the squares of X, or random variables, minus population mean over the number of observations in the population. Video The video displays the formula for population variance. Edward Volchok, PhD Page 6 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Sample variance is the mean of the sum of the squares of the random variables minus the sample mean, X-Bar, divided by the number of observations, or n. The formula of the sample variance, or s squared, is the sum of the squares of X, or random variables, minus sample mean, X-Bar, over the number of observations in the sample. Video The video displays the formula for sample variance. Edward Volchok, PhD Page 7 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Let’s calculate variance and standard deviation using Excel as if it were a simple handheld calculator. Video The video the words, “Using Excel as if it were a simple handheld calculator.” Edward Volchok, PhD Page 8 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step one is to find the mean. Video The video displays the words, “Step 1: Find the Mean.” Edward Volchok, PhD Page 9 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio In Cell B11, we enter the average function: Equal Sign, AVERAGE, open parenthesis, drag the cursor from Cell B3 through Cell B9, close parenthesis, and hit the Enter Key. In Cell B9, we used the SUM function to add the values of all the random variables. And, in Cell B10, we used the COUNT function to count the number of random variables. Video The video displays the AVERAGE function being entered into an Excel worksheet. Edward Volchok, PhD Page 10 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step 2: Subtract the mean from each random variable. Video The video displays the words, “Step 2: Subtract the mean from each random variable.” Edward Volchok, PhD Page 11 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio In Cell C3, we subtract the value of the mean from the random variable found in Cell B4. Please note: We designate the value of the mean using an absolute cell reference, $B$11. We then copy Cell C3 and paste it into Cells C4 through C8. Video The video displays an Excel worksheet where the value of each random variable being subtracted from the Mean. Edward Volchok, PhD Page 12 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step 3: We square the deviations from the mean. Video The video displays the words, “Step 3: We square the deviations from the mean.” Edward Volchok, PhD Page 13 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step 3 requires us to use the exponents function. Exponents indicate how many times the number is used in multiplication. We will square the deviations from the mean or multiply the base by itself. Video The video displays the following: “Exponents indicate how many times the number is used in multiplication. We will “square” the deviations from the mean (multiple the “base” by itself). 2 Also shown is an equation that shows that 2 equals 4. Edward Volchok, PhD Page 14 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio There are two ways to apply exponents in Excel. The first is using the POWER function. The POWER returns the results of the number raised to a power. For example, the five raised to the second power, or squared, returns 25, and 5 raised to the third power, or cubed, returns 125. Video The video displays information on the Excel’s POWER function. Edward Volchok, PhD Page 15 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The second way to apply exponents in Excel is to use the caret symbol. The caret symbol is found by typing Shift-6. To square 5, type, “Equal Sign, 5, carat, 2 and hit the Return Key.” Excel will return 25. To cube 5, type, “Equal Sign, 5, carat, 3 and hit the Return Key.” Excel will return 125. Video The video displays information on using the caret symbol to use exponents. Edward Volchok, PhD Page 16 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio To square the deviations from the mean, place the cursor in Cell D3. Type “Equal sign, C4, caret, 2, and hit the return key. Now copy Cell D3 into Cells D4 through D8. Video The video displays an Excel worksheet in which the deviations from the mean are squared in Cells D3 through D8. Edward Volchok, PhD Page 17 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step 4: Sum the squared deviations. Video The video displays the words, “Step 4: Sum the squared deviations.” Edward Volchok, PhD Page 18 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio To sum the squared deviations from the mean, go to Cell D9. Type Equal Sign, SUM, open parenthesis, drag the cursor from Cell D3 through D8, and hit the Enter Key. Excel returns 1,565.33. Video The video displays an Excel worksheet in which the sum of the squared deviations from the mean is being tallied. Edward Volchok, PhD Page 19 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Step 5: For a population, divide the sum of the squared deviations from the mean by N. For sample, divide by n – 1. Video The video displays the words, “Step 5: For a population, divide the sum of the squared deviations from the mean by N. For sample, divide by n – 1.” Edward Volchok, PhD Page 20 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio 2 In Cell D12, we calculate the population variance, σ , by entering the formula, Equal Sign, D9, or the sum of the squared deviations from the mean, divided by 2 D10, or n. In Cell D13, we calculate the sample variance, s , by entering the formula, Equal Sign, D9 divided by D11, or n - 1. Video 2 The video displays an Excel worksheet. In Cell D12, the population variance, σ , is 2 being calculated with the formula =D9/D10. In Cell D12, the sample variance, s , is being calculated with the formula =D9/D11. Edward Volchok, PhD Page 21 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The population standard deviation is the square root of population variance. The big advantage of standard deviation is that the result is in the same units as the mean. Video The video displays the formula for population standard deviation. Edward Volchok, PhD Page 22 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel The sample standard deviation is the square root of sample variance. Video The video displays the formula for population standard deviation. Edward Volchok, PhD Page 23 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio To calculate standard deviation we have a sixth step, which is to take the square root of variance. Video The video displays the words, “Step 6: Take the square root of variance.” Edward Volchok, PhD Page 24 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio To calculate square roots in Excel use the SQRT function. Video The video displays the words, “Use the SQRT Function.” Edward Volchok, PhD Page 25 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The syntax for the square root function is: Equal sign, SQRT, open parenthesis, number or cell reference, and close parenthesis. Video The video displays the words, “Syntax: =SQRT(number or cell reference).” Edward Volchok, PhD Page 26 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Equal sign, SQRT, open parenthesis, 25, and close parenthesis returns 5. Video The video displays the words, “=SQRT(25) returns 5.” Edward Volchok, PhD Page 27 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Equal sign, SQRT, open parenthesis, 4, and close parenthesis returns 2. Video The video displays the words, “=SQRT(4) returns 2.” Edward Volchok, PhD Page 28 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio In Cell D14, the square root of population variance, or the population standard deviation, is being calculated with the formula =SQRT(D12). Excel returns 16.15. In Cell D15, the square root of the sample variance, or the sample standard deviation, is being calculated with the formula =SQRT(D13). Excel returns 17.69. Video The video displays an Excel worksheet in which the population and sample standard deviations are calculated. Edward Volchok, PhD Page 29 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Using Excel’s building functions to calculate variance and standard deviation. This built-in functions save time as we can calculate variance or standard deviation in only one step. Video The video displays the words, “Using Excel’s Built-in Functions.” Edward Volchok, PhD Page 30 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio With the introduction of Excel 2010, Microsoft replaced the old population variance function, VARP, with the current population variance function VAR.P. The old formula, however, is still available. This allows worksheets developed with older version of Excel to function properly with the newer editions. Video The video displays the pre-Excel 2010 population variance formula and the current population variance formula. Edward Volchok, PhD Page 31 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Microsoft replaced the old sample variance function, VAR, with the current sample variance function VAR.S. Video The video displays the pre-Excel 2010 sample variance formula and the current sample variance formula. Edward Volchok, PhD Page 32 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Microsoft replaced the old population standard deviation function, STDEVP, with the current population standard deviation STDEV.P. Video The video displays the pre-Excel 2010 population standard deviation formula and the current population standard deviation formula. Edward Volchok, PhD Page 33 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Microsoft replaced the old sample standard deviation function, STDEV, with the current sample standard deviation function STDEV.S. Video The video displays the pre-Excel 2010 sample standard deviation formula and the current sample standard deviation formula. Edward Volchok, PhD Page 34 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Let’s calculate population and sample variance. In Cell B11 we type, “Equal Sign, VAR.P, open parenthesis, drag the cursor from Cell B3 to be B9, and hit the Return Key.” Excel returns the population variance, 260.89. In Cell B12 we type, “Equal Sign, VAR.S, open parenthesis, drag the cursor from cell B3 to be B9, and hit the Return Key.” Excel returns the sample variance, 313.07. Video The video displays the population variance and sample variance being calculated. Edward Volchok, PhD Page 35 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Let’s calculate population and sample standard deviation. In Cell B13 we type, “Equal Sign, STDEV.P, open parenthesis, drag the cursor from cell B3 to be B9, and hit the Return Key. Excel returns the population standard deviation, 16.15. In Cell B14 we type, “Equal Sign, STDEV.S, open parenthesis, drag the cursor from cell B3 to be B9, and hit the Return Key. Excel returns the sample standard deviation, 17.69. Video The video displays the population standard deviation and sample standard deviation being calculated. Edward Volchok, PhD Page 36 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio Excel has two other variance functions and two other standard deviation functions. The first variance function is VARA, which returns the variance of the supplied set of sample values that includes text and logical values. Video The video displays information on the VARA function. Edward Volchok, PhD Page 37 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The second variance function is VARPA, which returns the variance of the supplied set of population values that includes text and logical values. Video The video displays information on the VARPA function. Edward Volchok, PhD Page 38 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The first of the two standard deviation functions is STEDEVA, which returns the standard deviation of the supplied set of sample values that includes text and logical values. Video The video displays information on the STEDEVA function. Edward Volchok, PhD Page 39 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio The second of the two standard deviation functions is STEDEVPA, which returns the standard deviation of the supplied set of populations values that includes text and logical values. Video The video displays information on the STEDEVPA function. Edward Volchok, PhD Page 40 of 41 Var_StdDev_Transcript.docx Calculating the Variance and Standard Deviation Using Microsoft Excel Audio This has been our tutorial on how to use Microsoft Excel to calculate the variance and standard deviation. Video The video displays the “The End.” * Edward Volchok, PhD * Page 41 of 41 * Var_StdDev_Transcript.docx
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