Question

the ages (in years) of the 5 doctors at a local clinic are the following. 55, 39, 34, 52, 45. assuming that these ages constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.

Explanation:

Step1: Calculate the mean

The mean $\mu=\frac{55 + 39+34+52+45}{5}=\frac{225}{5}=45$.

Step2: Calculate the squared - differences

$(55 - 45)^2=100$, $(39 - 45)^2 = 36$, $(34 - 45)^2=121$, $(52 - 45)^2 = 49$, $(45 - 45)^2=0$.

Step3: Calculate the variance

The variance $\sigma^{2}=\frac{100 + 36+121+49+0}{5}=\frac{306}{5}=61.2$.

Step4: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{61.2}\approx7.82$.

Answer:

$7.82$