The error in Jerry's calculation is 4.84
The number of employees, N = 4
The mean is calculated as:
[tex]\mu = \frac{10+2+4+8}{4} \\\mu = \frac{24}{4} \\\mu = 6[/tex]
The formula for the standard deviation is:
[tex]SD =\sqrt{\frac{\sum{(x-\mu)^2}}{N} }[/tex]
This can be further calculated as:
[tex]SD = \sqrt{\frac{(10-6)^2+(2-6)^2+(4-6)^2+(8-6)^2}{4} }\\\\SD = \sqrt{\frac{4^2+(-4)^2+(-2)^2+(2)^2}{4} } \\\\SD = \sqrt{\frac{16+16+4+4}{4} } \\\\SD = \sqrt{\frac{40}{4} } \\\\SD = \sqrt{10} \\\\SD = 3.16[/tex]
Jerry thinks the Standard Deviation = 8
The true Standard Deviation = 3.16
Error = |True value - Measured value|
Error = |3.16 - 8|
Error = 4.84
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