It gives a good and accurate approximation when there is not much variation in the data.ħ. It applies to both positive and negative values.ħ. GM ≤ AM always for any set of data values.Ĥ. AM ≥ GM always for any set of data values.ģ. For a given set of data values x₁, x₂, x₃. , xₙ, the arithmetic mean = (x₁ + x₂ + x₃ +. It is calculated by raising the product of data values by reciprocal of the number of data values.Ģ. It is calculated by dividing the sum of data values by the number of data values.ġ. The differences between AM and GM that are mentioned in the previous section are summarized in the table below. The geometric mean (which is nothing but compounded growth) is used to calculate the average growth rates in finance.ĭifference Between Arithmetic Mean and Geometric Mean Table The arithmetic mean (which is nothing but average) is widely used in the fields of statistics, economics, history, and sociology. GM is more accurate when there is volatility in the data. Difference in Terms of AccuracyĪM is accurate when the data values are not skewed and are independent of each other. Difference in Terms of Ease of UseĪrithmetic mean is easy to use as it involves the sum whereas the geometric mean is difficult to use as it involves the product and taking roots. We can see that most of the data values are very far from AM whereas GM is not that much affected. For example, consider a set of data values with an outlier, say, 10, 12, 14, and 99. The geometric mean doesn't get affected much by the outlier whereas the arithmetic mean does. Difference in Terms of Effect of Outliers The geometric mean applies only to positive values whereas the arithmetic mean applies to both positive and negative values. We can see in the above example that 3.93 (GM) < 5 (AM). The geometric mean for a set of data values is always less than (or equal to) that of the arithmetic mean. Here are the differences between arithmetic mean and geometric mean in several ways. This is the difference between AM and GM in terms of meaning and formula. On the other hand, the geometric mean is the product of the values raised to the multiplicative inverse of the total number of values. In other words, the arithmetic mean is nothing but the average of the values. Thus, arithmetic mean is the sum of the values divided by the total number of values.
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