Question

The ages (in years) of the 6 employees at a particular computer store are 44, 46, 40, 34, 29, 41

Assuming that these ages constitute an entire population, find the standard deviation of the population. Round your answer to two decimal places.

Answer 1

step 1
compute the average: add the values and divide by 6
Average =(44+ 46+40+34+29+41)/6=39

step 2
Compute the deviations from the average
dev: (44-39)=5,
dev: (46-39)=7
dev: (40-39)=1
dev: (34-39)=-5
dev: (29-39)=-10
dev: (41-39)=2

step 3
Square the deviations and add
sum (dev^2): 5^2+7^2+1^2+-5^2+-10^2+2^2
sum (dev^2): 25+49+1+25+100+4-----> 204

step 4
Divide step #3 by the sample size=6
(typically you divide by sample size-1 to get the sample standard deviation,
but you are assuming the 6 values are the population,
so
no need to subtract 1, from the sample size.
This result is the variance
Variance =204/6=34

step 5
Standard deviation = sqrt(variance)
standard deviation= √(34)------> 5.83

the answer is
5.83