Answer:
The sample standard deviation for given data is 222.69
Step-by-step explanation:
We are given the following data set:
508, 657, 214, 958, 765, 449, 338, 497
Formula:
[tex]\text{Standard Deviation} = \sqrt{\displaystyle\frac{\sum (x_i -\bar{x})^2}{n-1}}[/tex]
where [tex]x_i[/tex] are data points, [tex]\bar{x}[/tex] is the mean and n is the number of observations.
[tex]Mean = \displaystyle\frac{\text{Sum of all observations}}{\text{Total number of observation}}[/tex]
[tex]Mean =\displaystyle\frac{4386}{8} = 548.25[/tex]
Sum of squares of differences =
1620.0625 + 11826.5625 + 111723.0625 + 167895.0625 + 46980.5625 + 9850.5625 + 44205.0625 + 2626.5625 = 396727.5
[tex]\text{Sample standard Deviation} = \sqrt{\dfrac{396727.5}{7}} =222.69[/tex]
The sample standard deviation for given data is 222.69
