Question

The 6 participants in a 200-meter dash had the following finishing times (in seconds): 27, 28, 27, 25, 24, 31 Assuming that these times constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.

Answer 1

Standard deviation of the population is 2.4

Explanation:

Finishing times of 6 participants in 200 meter dash has been given as 27, 28, 27, 25, 24, 31.

We have to calculate the standard deviation of the population formed by these timings.

Formula of standard deviation is

`\sigma=\sqrt{(\sum(x-\mu)^(2))/(n) }`

where
`\sigma` = standard deviation

`\mu` = mean of the data

n = number of scores in the sample

Mean of given data =
`(27+28+27+25+24+31)/(6)=27`

`\sum(x-\mu)^(2)=(27-27)^(2)+(28-27)^(2)+(27-27)^(2)+(25-28)^(2)+(24-27)^(2)+(31-27)^(2)`

=
`0+1+0+4+9+16`

= 30

Now
`(\sum(x-\mu)^(2))/(n)=(30)/(6)=5`

`\sigma=√(5)` = 2.236 ≈ 2.24

Therefore, standard deviation of the given data is 2.24