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7/2/08 Calculating Geometric Mean Using The Square Root Method GETTING STARTED Using the square root ( method to calculate geometric mean is the easiest way and only requires a basic function calculator with a key. Remember, this method can only be used when calculating results from 2 samples, 4 samples, 8 samples, 16 samples, etc. HERE’S HOW Let’s list the steps to follow. 1. For two samples: A. B. Multiply the two numbers together. Take the square root – You are done! Example: Calculate the geometric mean of these two lab results: 27 col/100 mL and 420 col/100 mL A. B. Multiply the two numbers: 27 X 420 = 11,340 Take the : 11,340 = 106.49 **When reporting FC results, always round the number up. You would report 107col/100mL (and one excursion!). 2. For four samples: A. B. C. Multiply all four numbers together Take the Take the again Example: Calculate the geometric mean of 45 col/100 mL; 220 col/100 mL; 1,200 col/100 mL mL; and 7/2/08 A. B. C. 45 X 220 X 2 X 1,200 = 23,760,000 23,760,000 = 4,874.4 4,874.4 = 69.81 - Report 70 col/100 mL NOTE If you have a “less than” result, just use the number. 2 use 2; 5 use 5; 10 use 10. If a zero is reported for some reason, use 1 in the calculation; then call the lab and tell them they are not calculating their results correctly. There should never be a zero. If you get a “greater than” result, just use the number. 2,000 use 2,000; 5,400 use 5,400. The log method will also work on 2, 4, 8, 16, 32 . . . etc. sample results. OTHER CONSIDERATIONS You can use the for 8 samples; the only difference would be to take the square root three times. For 16 samples, take the square root 4 times. WARNING Basic function calculators may not have enough memory to hold very large numbers when you perform the first step above (Step A). So you may have to perform a “pretreatment” step to get the numbers to fit. Example: The four results are: 1,200; 460; 180; and 2,200. 1. Divide each number by (choose anything) say 100. 1,200 = 12 100 460 = 4.6 100 180 = 1.8 100 2,200 = 22 100 A. Multiply - 12 X 4.6 X 1.8 X 22 = 2,185.92 B. Take the square root - 2,185.92 C. Take the square root again - 46.75 2. The final step is putting back the number we used in Step 1. 6.84 X 100 = 684 col/100 mL = 46.75 = 6.84 7/2/08 NOTE In Step 1 you can divide by any number you choose: 100 or 1,000 or 10,000 or 4,736 if you want. Just remember to multiply that number back in at the end of Step C. Here are some practice problems with the answers below. Calculate the geometric means using the square root method. 1) 10 165 1,250 5 2) 2,400 1,800 1 480 3) 2,600 10 2) 214 3) 162 Answers. 1) 57