Answer:
The standard deviation of the data set is [tex]\sigma=10[/tex]
Step-by-step explanation:
The formula for standard deviation is [tex]\sigma=\sqrt{\frac{1}{N}\sum_{n=1}^{\infty}(x_i-\mu)^2 }[/tex] where you are basically taking the mean of the data set ([tex]\mu[/tex]), find the mean of the squared differences from the observed values and mean ([tex](x_i-\mu)^2[/tex]), and square root the result:
Mean:
[tex]\mu=\frac{36+18+12+10+9}{5}=\frac{85}{5}=17[/tex]
Average of squared differences (variance):
[tex]\frac{1}{N}\sum_{n=1}^{\infty}(x_i-\mu)^2=\frac{(36-17)^2+(18-17)^2+(12-17)^2+(10-17)^2+(9-17)^2}{5}=\frac{500}{5}=100[/tex]
Standard deviation:
[tex]\sigma=\sqrt{100}=10[/tex]
This means that the standard deviation of the data set is 10, which tells us that the values of the data set, on average, are separated by 10.
