Question

The weights (in grams) of the contents of several small bottles are 4, 2, 5, 4, 5, 2 and 6. What is the sample variance?

a.6.92
b.4.80
c.1.96
d.2.33

Answer 1

To find the sample variance, calculate the mean of the data and subtract it from each weight. Square the differences, sum them up, and divide by (n - 1). The sample variance of the given data is 2.

Step-by-step explanation:

To find the sample variance, we can use the formula:

Variance = (Σ(x - μ)²) / (n - 1)

First, calculate the mean of the data. Add up all the weights and divide by the number of data points:

Mean = (4 + 2 + 5 + 4 + 5 + 2 + 6) / 7 = 4

Next, subtract the mean from each weight and square the result:

(4 - 4)² = 0

(2 - 4)² = 4

(5 - 4)² = 1

(4 - 4)² = 0

(5 - 4)² = 1

(2 - 4)² = 4

(6 - 4)² = 4

Add up all the squared differences:

0 + 4 + 1 + 0 + 1 + 4 + 4 = 14

Finally, divide the sum by (n - 1), where n is the number of data points:

Variance = 14 / (7 - 1) = 2

Therefore, the sample variance is 2.