Question

Find the sample variance and standard deviation.22, 15, 3, 9, 8Choose the correct answer below. Fill in the answer box to complete your choice.(Type an integer or a decimal. Round to one decimal place as needed.)O A. S2=B. o

Answer 1

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!!!