Question

the 6 participants in a 200 - meter dash had the following finishing times (in seconds). 32, 25, 26, 24, 24, 25. assuming that these times constitute an entire population, find the standard deviation of the population. round your answer to two decimal places.

Explanation:

Step1: Calculate the mean

The data set is $32,25,26,24,24,25$. The mean $\mu=\frac{32 + 25+26+24+24+25}{6}=\frac{156}{6}=26$.

Step2: Calculate the squared - differences

$(32 - 26)^2=36$, $(25 - 26)^2 = 1$, $(26 - 26)^2=0$, $(24 - 26)^2 = 4$, $(24 - 26)^2=4$, $(25 - 26)^2 = 1$.

Step3: Calculate the variance

The variance $\sigma^{2}=\frac{36+1 + 0+4+4+1}{6}=\frac{46}{6}\approx7.67$.

Step4: Calculate the standard deviation

The standard deviation $\sigma=\sqrt{\frac{46}{6}}\approx2.83$.

Answer:

$2.83$