A data set contains the following six values. 10, 18, 13, 30, 23, 18 (Round the intermediate values to 3 decimal places. Round your final answers to 3 decimal places) Find the population standard deviation. Blank 1 Find the population variance. Blank 2
Question
A data set contains the following six values.
10, 18, 13, 30, 23, 18
(Round the intermediate values to 3 decimal places. Round your final answers to 3 decimal places)
Find the population standard deviation. Blank 1 Find the population variance. Blank 2
Solution
To find the population standard deviation and variance, follow these steps:
Step 1: Calculate the mean (average) of the data set. Mean = (10 + 18 + 13 + 30 + 23 + 18) / 6 = 18.667
Step 2: Subtract the mean from each data point and square the result. (10 - 18.667)^2 = 74.889 (18 - 18.667)^2 = 0.444 (13 - 18.667)^2 = 32.222 (30 - 18.667)^2 = 128.222 (23 - 18.667)^2 = 18.889 (18 - 18.667)^2 = 0.444
Step 3: Add up all the squared results. Sum = 74.889 + 0.444 + 32.222 + 128.222 + 18.889 + 0.444 = 255.111
Step 4: Divide the sum by the number of data points to get the variance. Variance = 255.111 / 6 = 42.518 (Blank 2)
Step 5: Take the square root of the variance to get the standard deviation. Standard Deviation = sqrt(42.518) = 6.522 (Blank 1)
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