Let’s consider a manufacturing firm that runs a series of 10 tests to determine whether there is a variation in the quality of its products. The data points for the 10 tests are 8.4, 8.5, 9.1, 9.3, 9.4, 9.5, 9.7, 9.7, 9.9, and 9.9.
First, calculate the mean of the observed data. (8.4 + 8.5 + 9.1 + 9.3 + 9.4 + 9.5 + 9.7 + 9.7 + 9.9 + 9.9) / 10, which equals 93.4 / 10 = 9.34.
Second, calculate the variance of the set. Variance is the spread between data points and is calculated as the sum of the squares of the difference between each data point and the mean divided by the number of observations. The first difference square will be calculated as (8.4 - 9.34)2 = 0.8836, the second square of difference will be (8.5 - 9.34)2 = 0.7056, the third square can be calculated as (9.1 - 9.34)2 = 0.0576, and so on. The sum of the different squares of all 10 data points is 2.564. The variance is, therefore, 2.564 / 10 = 0.2564.
Third, calculate the standard deviation, which is simply the square root of the variance. So, the standard deviation = √0.2564 = 0.5064.
Fourth, calculate three-sigma, which is three standard deviations above the mean.
https://www.investopedia.com/terms/t/three-sigma-limits.asp
No comments:
Post a Comment