For the following set of data, find the population standard deviation, to the nearest hundredth.
165, 68, 121, 41, 59, 116, 120
To find the population standard deviation, we first need to find the mean of the data set:
Mean = (165 + 68 + 121 + 41 + 59 + 116 + 120) / 7 = 90
Next, we calculate the squared difference between each data point and the mean:
(165-90)^2 = 75^2 = 5625
(68-90)^2 = (-22)^2 = 484
(121-90)^2 = 31^2 = 961
(41-90)^2 = (-49)^2 = 2401
(59-90)^2 = (-31)^2 = 961
(116-90)^2 = 26^2 = 676
(120-90)^2 = 30^2 = 900
Now we calculate the variance by adding up all the squared differences and dividing by the number of data points:
Variance = (5625 + 484 + 961 + 2401 + 961 + 676 + 900) / 7 = 2911.43
Lastly, we find the square root of the variance to get the population standard deviation:
Population Standard Deviation = √2911.43 ≈ 53.96
Therefore, the population standard deviation of the data set is 53.96 (rounded to the nearest hundredth).