First, calculate the average of the data set. Then, calculate the deviations of each data point from the mean and square the result of each. Next, calculate the mean of those values, which gives us the variance of the data set. Finally, take the square root of the variance, which gives us the standard deviation.
The average of the data set, is:
[tex]\frac{63+79+72+77}{4}=72.75[/tex]
The squares of the deviations of each data point, are:
[tex]\begin{gathered} (63-72.75)^2=(-9.75)^2=95.0625 \\ (79-72.75)^2=(6.25)^2=39.0625 \\ (72-72.75)^2=(-0.75)^2=0.5625 \\ (77-72.75)^2=(4.25)^2=18.0625 \end{gathered}[/tex]
The variance of the data set is:
[tex]\sigma^2=\frac{95.0625+39.0625+0.5625+18.0625}{4}=38.1875[/tex]
The standard deviation of the data set, is:
[tex]\sigma=\sqrt[]{38.1875}=6.1796\ldots[/tex]
To the nearest hundredth, the standard deviation is 6.18.
Therefore, the answer is:
[tex]6.18[/tex]
