Suppose a sample of five retail stores' monthly profits are: $4,000, $7,000, $5,000, $3,000, and $1,000. What will the sample variance of stores profits be?
A) $20 million
B) $4 million
C) $10 million
D) $5 million

Question

Quizplus · Accepted Answer

To find the sample variance, we first need to find the sample mean:
Mean = ($4,000 + $7,000 + $5,000 + $3,000 + $1,000) / 5 = $4,000

Next, we calculate the deviation of each data point from the mean:
($4,000 - $4,000) = 0
($7,000 - $4,000) = $3,000
($5,000 - $4,000) = $1,000
($3,000 - $4,000) = -$1,000
($1,000 - $4,000) = -$3,000

We square each deviation:
0^2 = 0
3,000^2 = 9,000,000
1,000^2 = 1,000,000
(-1,000)^2 = 1,000,000
(-3,000)^2 = 9,000,000

We sum the squared deviations:
0 + 9,000,000 + 1,000,000 + 1,000,000 + 9,000,000 = 20,000,000

Finally, we divide by n-1 (where n is the sample size):
20,000,000 / 4 = 5,000,000

Therefore, the sample variance is $5 million.

Suppose a Sample of Five Retail Stores' Monthly Profits Are