Question

A rancher’s herd of 250 sheep grazes over a 40-acre pasture. He would like to find out how many sheep are grazing on each acre of the pasture at any given time, so he has some images of the pasture taken by the state department of agriculture’s aerial photography division. Here are three samples of the images.

Sample 1 4
Sample 2 1
Sample 3 9
How do the sample statistics compare to the population mean and standard deviation?

Answer 1

5

Explanation:

Answer 2

The population mean is 4.67 and the standard deviation is 4.04.

Mean = (4 + 1 + 9)/3 = 4.67

Variance

subtract the mean from each value:

4 - 4.67 = -0.67

1 - 4.67 = -3.67

9 - 4.67 = 4.33

square each of these:

(-0.67)2 = 0.4489

(-3.67)2 = 13.4689

(4.33)2 = 18.7489

add these together and divide by 3:

(0.4489 + 13.4689 + 18.7489)/3 = 32.6667/3 = 10.9.

Standard deviation = square root of variance = 3.3.

Explanation: