SCANLON SCIENCE



Intro to Statistics: Calculating Standard DeviationIn this article, we'll learn how to calculate standard deviation "by hand". Interestingly, in the real world no statistician would ever calculate standard deviation by hand. The calculations involved are somewhat complex, and the risk of making a mistake is high. Also, calculating by hand is slow. Very slow. This is why statisticians rely on spreadsheets and computer programs to crunch their numbers.So what's the point of this article? Why are we taking time to learn a process statisticians don't actually use? The answer is that learning to do the calculations by hand will give us insight into how standard deviation really works. This insight is valuable. Instead of viewing standard deviation as some magical number our spreadsheet or computer program gives us, we'll be able to explain where that number comes from.The Symbolss = standard deviation for sample? = standard deviation for populationN or n = number of data points usedxi = data pointμ = mean for population dataxbar = mean for sample dataΣ = summation (sum)The StepsStep 1: Find the meanStep 2: For each data point, find the square of its distance to the mean and take the absolute valueStep 3: Sum the values from Step 2Step 4: Divide by the number of data pointsStep 5: Take the square root511038918605500Example Problem: Data Set: 6, 2, 3, 1Step 1: Find the mean (μ)Step 2: For each data point, find the square of its distance to the mean and take the absolute value (|x – μ|2)Step 3: Sum the values from Step 2 (Σ|x – μ|2)Step 4: Divide by the number of data points ((Σ|x – μ|2)/N)Step 5: Take the square root √((Σ|x – μ|2)/N)Practice Problem 1: Data Set: 34, 23, 35, 23, 23, 25, 26, 23Practice Problem 2:Data Set: 100, 97, 93, 86, 87, 94, 94, 98Practice Problem 3: Data Set: 34, 35, 34, 40, 38, 37, 34, 30Practice Problem 4: Data Set: 76, 87, 74, 72, 69, 80, 84, 82 ................
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