Suppose you are trying to figure out how many coffees you have purchased since y

ID: 3202033 • Letter: S

Question

Suppose you are trying to figure out how many coffees you have purchased since you turned 18. You note that your coffee purchases have been pretty consistent since you turned 18 so you figure you will count the number of coffees you purchase per week currently and use this number to estimate the total number of coffee purchases. You keep records on the number of coffees you buy for 5 weeks and figure that this will suffice. The following table shows your number of coffees purchased per week over those 5 weeks.

What is the sample variance of coffees purchased?

Week 1 2 3 4 5 Coffees Purchased 15 100 20 25 15

Explanation / Answer

Solution:

Here, we have to find the sample variance. The formula for sample variance is given as below:

Sample variance = S^2 = (x - mean)^2*/ (n – 1)

Calculation table is given as below:

Week

(X - mean)

(X - mean)^2

-20

400

100

4225

-15

225

-10

100

-20

400

Total

175

5350

Variance =

1337.5

(x - mean)^2 = 5350

Sample variance = S^2 = (x - mean)^2*/ (n – 1)

We are given n = 5

Sample variance = S^2 = 5350/4 = 1337.5 or 1338 approximately

Answer: 1338