Answer
A) Variance = σ² = 212.1
B) Standard Deviation = σ = 14.6
Step-by-step explanation
The standard deviation is the square root of variance. And variance is an average of the squared deviations from the mean.
Mathematically for a sample distribution,
Variance = [Σ(x - xbar)²/(N - 1)]
Standard deviation = σ = √[Σ(x - xbar)²/(N - 1)]
x = each variable
xbar = mean
N = number of variables
The mean is the average of the distribution. It is obtained mathematically as the sum of variables divided by the number of variables.
Mean = (Σx)/N
x = each variable
Σx = Sum of the variables
N = number of variables
Σx = 22 + 15 + 3 + 9 + 8 = 57
N = 5
Mean = xbar = (Σx)/N = (57/5) = 11.4
Variance = [Σ(x - xbar)²/(N - 1)]
Σ(x - xbar)² = (22 - 11.4)² + (15 - 11.4)² + (3 - 11.4)² + (9 - 11.4)² + (8 - 11.4)²
Σ(x - xbar)² = (10.6)² + (3.6)² + (-8.4)² + (-2.4)² + (-3.4)²
Σ(x - xbar)² = 112.36 + 12.96 + 705.6 + 5.76 + 11.56
Σ(x - xbar)² = 848.24
N - 1 = 5 - 1 = 4
Variance = [Σ(x - xbar)²/(N - 1)]
Variance = (848.24/4) = 212.06 = 212.1
Standard deviation = σ = √[Σ(x - xbar)²/(N - 1)]
Standard deviation = σ = √(212.06) = 14.6
Hope this Helps!!!