Answer:
Explanation:
σ = sqrt [ Σ ( xi - μ )^2 / N ]
where:
σ is the standard deviation
Σ is the sum of the values
xi is the value of the i-th observation
μ is the mean of the population
N is the number of observations
First, we need to find the mean of the population:
μ = (20 + 30 + 13 + 10 + 22 + 37) / 6
μ = 132 / 6
μ = 22
Next, we can calculate the deviations of each observation from the mean:
20 - 22 = -2
30 - 22 = 8
13 - 22 = -9
10 - 22 = -12
22 - 22 = 0
37 - 22 = 15
Then, we square each deviation:
(-2)^2 = 4
8^2 = 64
(-9)^2 = 81
(-12)^2 = 144
0^2 = 0
15^2 = 225
We add up the squared deviations:
4 + 64 + 81 + 144 + 0 + 225 = 518
We divide by the number of observations and take the square root:
σ = sqrt [ Σ ( xi - μ )^2 / N ]
σ = sqrt (518 / 6)
σ ≈ 10.72
Therefore, the standard deviation of the population is approximately 10.72 dollars.