After collecting data, one of the first things to do is analyze it. This usually means finding its mean, standard deviation, and standard error. This article will show you how.
Steps
Method 1 of 4: The data
Step 1. Get a series of numbers to analyze
This information is referred to as a sample.
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For example, a test was given to a class of 5 students and the results are 12, 55, 74, 79 and 90.
Method 2 of 4: The Average
Calculate Mean, Standard Deviation, and Standard Error Step 2 Step 1. Calculate the average
Add all the numbers and divide by the population size:
- Mean (μ) = ΣX / N, where Σ is the sum (addition) symbol, xthe denotes any single number and N is the size of the population.
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In our case, the mean μ is simply (12 + 55 + 74 + 79 + 90) / 5 = 62.
Method 3 of 4: The Standard Deviation
Calculate Mean, Standard Deviation, and Standard Error Step 3 Step 1. Calculate the standard deviation
This represents the distribution of the population. Standard deviation = σ = sq rt [(Σ ((X-μ) ^ 2)) / (N)].
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In the given example, 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 had been the sample standard deviation, you would have had to divide by n-1, the sample size minus 1.)
Method 4 of 4: The Standard Error of the Mean
Calculate Mean, Standard Deviation, and Standard Error Step 4 Step 1. Calculate the standard error (of the mean)
This is an estimate of how close the sample mean is to the population mean. The larger the sample, the lower the standard error, and the closer the sample mean will be to the population mean. Divide the standard deviation by the square root of N, the sample size Standard error = σ / sqrt (n)
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So, in the example above, if the 5 students were a sample of a class of 50 students and the 50 students had a standard deviation of 17 (σ = 21), the standard error = 17 / sqrt (5) = 7.6.
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