Following are the ages (in years) of 6 people in a group: 25, 30, 35, 40, 45 and 50. What is the standard deviation of their ages (rounded to two decimal places)?

Correct option is C

Given:

Ages = 25, 30, 35, 40, 45, 50 (n = 6)

Formula Used:
Population Mean:$$\bar{x}=\frac{\sum x_i}{n}$$​​
Population Variance:$$\sigma^2=\frac{\sum (x_i-\bar{x})^2}{n}$$​​
Population Standard Deviation: $$\sigma=\sqrt{\sigma^2}$$​​

Solution:
​$$\bar{x}=\frac{25+30+35+40+45+50}{6}=\frac{225}{6}=37.5$$​​

Squared deviations:
​$$(25-37.5)^2=156.25,\ (30-37.5)^2=56.25,\ (35-37.5)^2=6.25,$$​​
​$$(40-37.5)^2=6.25,\ (45-37.5)^2=56.25,\ (50-37.5)^2=156.25$$​​

​$$\sum (x_i-\bar{x})^2=437.5$$​​

​$$\sigma^2=\frac{437.5}{6}=72.9167$$​​

​$$\sigma=\sqrt{72.9167}\approx 8.54$$​​