Question

Unit sales for new product ABC have varied in the first seven months of this year as follows:

Month	Jan	Feb	Mar	Apr	May	Jun	Jul
Unit Sales	145	492	319	265	389	321	180

What is the (population) standard deviation of the data?

Please round your answer to the nearest integer.

Note that the correct answer will be evaluated based on the full-precision result you would obtain using Excel.

Answer 1

Solution:

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

Population Mean = µ = ∑ X/n

Population Variance = σ² = ∑[ (X - mean)^2]/n

Population Standard deviation = σ = Sqrt(S²) = Sqrt(Variance)

The calculation table is given as below:

Month	X	(X - mean)^2
1	145	24514.6033
2	492	36263.0517
3	319	303.756098
4	265	1337.467298
5	389	7643.760098
6	321	377.470498
7	180	14779.6053
Total	2111	85219.71429

From above table, we have

n = 7

Population Mean = µ = 2111/7 = 301.5714

Population Variance = σ² = 85219.71429/7 = 12174.2449

Population Standard deviation = σ = Sqrt(12174.2449) = 110.3369607

What is the (population) standard deviation of the data?

Answer: 110

(Rounded to nearest integer)