For the following set of data, find the population standard deviation, to the nearest hundredth.
Data Frequency
11 5
12 9
16 7
18 8
21 4
23 3
25 1
32 1
33 5
To find the population standard deviation, we need to first calculate the population mean:
Population mean = (11 x 5) + (12 x 9) + (16 x 7) + (18 x 8) + (21 x 4) + (23 x 3) + (25 x 1) + (32 x 1) + (33 x 5)
= 1060 / 43
≈ 24.65
Next, we need to calculate the variance:
Variance = [(11 - 24.65)^2 x 5] + [(12 - 24.65)^2 x 9] + [(16 - 24.65)^2 x 7] + [(18 - 24.65)^2 x 8] + [(21 - 24.65)^2 x 4] + [(23 - 24.65)^2 x 3] + [(25 - 24.65)^2 x 1] + [(32 - 24.65)^2 x 1] + [(33 - 24.65)^2 x 5]
= 2653.24
Finally, we can find the population standard deviation by taking the square root of the variance:
Population standard deviation = √(2653.24)
≈ 51.50
Therefore, the population standard deviation is approximately 51.50.