Question

One random sample of five customers purchased these numbers of magazines: 1, 6, 3, 2, 3. Find the sample mean, sample variance, and sample deviation

Answer 1

The formulas for mean, variance, and standard deviation for sample are given as below:

Sample Mean = X̄ = ∑ X/n

Sample Variance = S2 = ∑[ (X - mean)^2]/(n - 1)

Sample Standard deviation = S = Sqrt(S2) = Sqrt(Variance)

The calculation table is given as below:

No.	X	(X - mean)^2
1	1	4
2	6	9
3	3	0
4	2	1
5	3	0
Total	15	14

From above table, we have

n = 5

Sample Mean = X̄ = 15/5 = 3

Sample Variance = S2 = 14/(5 - 1) = 14/4 = 3.5

Sample Standard deviation = S = sqrt(3.5) = 1.87