Answer:
a) s = 4.6
b) s = 4.6
Step-by-step explanation:
We are given the following in he question:
a) 4, 13, 5, 14, 10
We have to calculate sample standard deviation.
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{46}{5} = 9.2[/tex]
Sum of squares of differences = 82.8
[tex]s = \sqrt{\dfrac{82.8}{4}} = 4.6[/tex]
b) Adding three to each observation
7, 16, 8, 17, 13
[tex]Mean =\displaystyle\frac{61}{5} = 12.2[/tex]
Sum of squares of differences = 82.8
[tex]s = \sqrt{\dfrac{82.8}{4}} = 4.6[/tex]
Thus, the two standard deviation are same.
