Standard Deviation Calculator
Calculate standard deviation, variance, mean, and z-scores with step-by-step work.
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Input Numbers
8 numbers parsed
Results
Count (N)8
Sum144
Mean18
Min10
Max23
Range13
Population Variance24
Population Std Dev4.898979
Sample Variance27.428571
Sample Std Dev5.237229
Step-by-Step Work
Step 1: Mean = Sum / N = 144 / 8 = 18
Step 2: Squared differences from mean:
(10 - 18)^2 = 64
(12 - 18)^2 = 36
(23 - 18)^2 = 25
(23 - 18)^2 = 25
(16 - 18)^2 = 4
(23 - 18)^2 = 25
(21 - 18)^2 = 9
(16 - 18)^2 = 4
Step 3: Sum of squared diffs = 192
Step 4 (Population): Variance = 192 / 8 = 24
Population Std Dev = sqrt(24) = 4.898979
Step 4 (Sample): Variance = 192 / 7 = 27.428571
Sample Std Dev = sqrt(27.428571) = 5.237229
Z-Scores (Population)
x = 10
z = -1.632993
x = 12
z = -1.224745
x = 23
z = 1.020621
x = 23
z = 1.020621
x = 16
z = -0.408248
x = 23
z = 1.020621
x = 21
z = 0.612372
x = 16
z = -0.408248
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