Question

For the following set of scores: 1,4,3,5,7

(a) If the scores are a population, what are the variance and standard deviation?
(b) If the scores are a sample, what are the variance and standard deviation?

Answer 1

To find the variance of a population, calculate the average of the squared differences between each score and the mean. To find the standard deviation, take the square root of the variance.

Step-by-step explanation:

(a) To find the variance of a population, you need to calculate the average of the squared differences between each score and the mean.

Using the formula:

Variance = (1/N) * Σ(x_i - mean)^2

where N is the number of scores, Σ represents the summation, x_i represents each score, and mean is the average of the scores.

For the given population, the mean is (1+4+3+5+7)/5 = 4, so the variance would be ((1-4)^2 + (4-4)^2 + (3-4)^2 + (5-4)^2 + (7-4)^2)/5 = 4.

(b) To find the standard deviation of a population, you need to take the square root of the variance. So, in this case, the standard deviation would be √4 = 2.