A random sample of 5 data points, 4, 6, 8, 10 and 12, was collected. Find the standard deviation of this sample.
Answer
Step 4: Take the square root of the result from step 3. So, \(\sqrt{8} = 2.83\).
Step 1 ：Step 1: Calculate the mean (average) of the data set. The formula for the mean is: \(\frac{\sum x}{n}\), where \(\sum x\) is the sum of all data points and \(n\) is the number of data points. So, \(\frac{4+6+8+10+12}{5} = 8\).
Step 2 ：Step 2: Subtract the mean from each data point and square the result. The results are: \((4-8)^2 = 16, (6-8)^2 = 4, (8-8)^2 = 0, (10-8)^2 = 4, (12-8)^2 = 16\).
Step 3 ：Step 3: Calculate the mean of these squared differences. So, \(\frac{16+4+0+4+16}{5} = 8\).
Step 4 ：Step 4: Take the square root of the result from step 3. So, \(\sqrt{8} = 2.83\).
