Difference between revisions of "Calculate Mean, Standard Deviation, and Standard Error"
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After collecting data, often times the first thing you need to do is analyze it. This usually entails finding the mean, the standard deviation, and the standard error of the data. This article will show you how it's done. | After collecting data, often times the first thing you need to do is analyze it. This usually entails finding the mean, the standard deviation, and the standard error of the data. This article will show you how it's done. | ||
| − | [[Category:Probability and Statistics]] | + | [[Category: Probability and Statistics]] |
== Steps == | == Steps == | ||
=== Cheat Sheets === | === Cheat Sheets === | ||
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=== The Data === | === The Data === | ||
# Obtain a set of numbers you wish to [[Analyze Debt to Equity Ratio|analyze]]. This information is referred to as a sample. | # Obtain a set of numbers you wish to [[Analyze Debt to Equity Ratio|analyze]]. This information is referred to as a sample. | ||
| − | #*For example, a test was given to a class of 5 students, and the test results are 12, 55, 74, 79 and 90. | + | #*For example, a test was given to a class of 5 students, and the test results are 12, 55, 74, 79 and 90. |
=== The Mean === | === The Mean === | ||
#Calculate the [[Calculate the Mean|mean]]. Add up all the numbers and divide by the population size: | #Calculate the [[Calculate the Mean|mean]]. Add up all the numbers and divide by the population size: | ||
| − | #*Mean (μ) = ΣX/N, where Σ is the summation (addition) sign, x<sub>i</sub> is each individual number, and N is the population size. | + | #*Mean (μ) = ΣX/N, where Σ is the summation (addition) sign, x<sub>i</sub> is each individual number, and N is the population size. |
| − | #*In the case above, the mean μ is simply (12+55+74+79+90)/5 = 62. | + | #*In the case above, the mean μ is simply (12+55+74+79+90)/5 = 62. |
=== The Standard Deviation === | === The Standard Deviation === | ||
# Calculate the standard deviation. This represents the spread of the population. <br>Standard deviation = σ = sq rt [(Σ((X-μ)^2))/(N)]. | # Calculate the standard deviation. This represents the spread of the population. <br>Standard deviation = σ = sq rt [(Σ((X-μ)^2))/(N)]. | ||
| − | #*For the example given, the standard deviation is sqrt[((12-62)^2 + (55-62)^2 + (74-62)^2 + (79-62)^2 + (90-62)^2)/(5)] = 27.4. (Note that if this was the sample standard deviation, you would divide by n-1, the sample size minus 1.) | + | #*For the example given, the standard deviation is sqrt[((12-62)^2 + (55-62)^2 + (74-62)^2 + (79-62)^2 + (90-62)^2)/(5)] = 27.4. (Note that if this was the sample standard deviation, you would divide by n-1, the sample size minus 1.) |
=== The Standard Error of the Mean === | === The Standard Error of the Mean === | ||
# Calculate the standard error (of the mean). This represents how well the sample mean approximates the population mean. The larger the sample, the smaller the standard error, and the closer the sample mean approximates the [[Focus Website Promotion on Country Internet Population|population]] mean. Do this by dividing the standard deviation by the square root of N, the sample size.<br>Standard error = σ/sqrt(n) | # Calculate the standard error (of the mean). This represents how well the sample mean approximates the population mean. The larger the sample, the smaller the standard error, and the closer the sample mean approximates the [[Focus Website Promotion on Country Internet Population|population]] mean. Do this by dividing the standard deviation by the square root of N, the sample size.<br>Standard error = σ/sqrt(n) | ||
| − | #*So for the example above, if this were a sampling of 5 students from a class of 50 and the 50 students had a standard deviation of 17 (σ = 21), the standard error = 17/sqrt(5) = 7.6. | + | #*So for the example above, if this were a sampling of 5 students from a class of 50 and the 50 students had a standard deviation of 17 (σ = 21), the standard error = 17/sqrt(5) = 7.6. |
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== Tips == | == Tips == | ||
