Answer:
The standard deviation for given sample is 11.94
Step-by-step explanation:
We are given the following sample of count of bacteria:
41, 62, 45, 48, 69
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{265}{5} = 53[/tex]
Deviation from mean:
-12, 9, -8, -5, 16
Sum of squares of differences =
144 + 81 + 64 + 25 + 256 = 570
[tex]s = \sqrt{\frac{570}{4}} = 11.94[/tex]
Thus, the standard deviation for given sample is 11.94
