The reason for calculating with “1.05” and “1.10” instead of “0.05” and “0.10” is that 0747)^4” you get the amount as if sales went up. This result is meaningful in that sense that it is the average, annual growth. If on the other hand you calculate =GEO.MEAN(1.05 1.05 1.10 1.10) -1, you get. This result is not meaningful, in that sense that you can’t do anything with it. This is equivalent to the harmonic mean of 50 and 70, and so can be calculated in Excel as HARMEAN(50,70), which is HARMEAN(G7:G8) from Figure 2.Ġ.070711 is calculated as =GEO.MEAN(.05. Since the distance for the whole trip is 2 d, your average speed for the whole trip is The harmonic mean can be used to calculate an average speed, as described in Example 6.Įxample 6: If you go to your destination at 50 mph and return at 70 mph, what is your average rate of speed?Īssuming the distance to your destination is d, the time it takes to reach your destination is d/50 hours and the time it takes to return is d/70, for a total of d/50 + d/70 hours. 0747.ĭefinition 5: The harmonic mean of the data set S is calculated by the formula The same annual growth rate of 7.47% can be obtained in Excel using the formula GEOMEAN(H7:H10) – 1 =. The annual growth rate r is that amount such that (1+ r) 4 = 1.334. If sales in year 1 are $1 then sales at the end of the 4 years are (1 +. This statistic is commonly used to provide a measure of the average rate of growth as described in Example 5.Įxample 5: Suppose the sales of a certain product grow 5% in the first two years and 10% in the next two years, what is the average rate of growth over the 4 years? This function is equivalent to MODE.ĭefinition 4: The geometric mean of the data set S is calculated by The function MODE.SNGL is also provided with versions of Excel starting with Excel 2010. When we highlight C19:C20 and enter the array formula =MODE.MULT(C3: C10) and then press Ctrl-Alt-Enter, we see that both modes are displayed. Starting with Excel 2010 the array function MODE.MULT is provided which is useful for multimodal data by returning a vertical list of modes. We consider a random variable x and a data set S = .