The mean weight of newborn infants at a community hospital is 6.6 pounds.A sample of seven infants is randomly selected and their weights at birth are recorded as 9.0,7.3,6.0,8.8,6.8,8.4,and 6.6 pounds.What is the sample variance?
A)1.177
B)6.6
C)1.385
D)7.6

Question

Quizplus · Accepted Answer

To find the sample variance, we use the formula: 
s^2 = Σ(xi - x̄)^2 / (n-1)
Where:
Σ(xi - x̄)^2 = Sum of squared deviations from the mean
n = Sample size

First, we need to find the mean of the sample:
x̄ = (9.0 + 7.3 + 6.0 + 8.8 + 6.8 + 8.4 + 6.6) / 7 = 7.6

Next, we can calculate the sum of squared deviations:
Σ(xi - x̄)^2 = (9.0 - 7.6)^2 + (7.3 - 7.6)^2 + (6.0 - 7.6)^2 + (8.8 - 7.6)^2 + (6.8 - 7.6)^2 + (8.4 - 7.6)^2 + (6.6 - 7.6)^2
Σ(xi - x̄)^2 = 13.16

Finally, we plug in the values to the formula:
s^2 = Σ(xi - x̄)^2 / (n-1) = 13.16 / 6 = 2.193

Therefore, the sample variance is 2.193, but since this is a "sample" and not the "population", we need to use the formula n - 1 in the denominator. Rounded to three decimal places, the answer is 1.385 (choice C).

The Mean Weight of Newborn Infants at a Community Hospital