To calculate the variance for a population, you need to follow a few steps. Let’s say you have a set of scores: 4, 8, 6, 5, and 3. Here’s how to compute the variance:
- Find the mean: Add all the scores together and divide by the number of scores. For our set: (4 + 8 + 6 + 5 + 3) / 5 = 26 / 5 = 5.2
- Calculate the squared differences: Subtract the mean from each score, square the result, and then list those values:
- (4 – 5.2)² = 1.44
- (8 – 5.2)² = 7.84
- (6 – 5.2)² = 0.64
- (5 – 5.2)² = 0.04
- (3 – 5.2)² = 4.84
- Find the average of those squared differences: Add all the squared differences together and divide by the number of scores (since we are calculating population variance):
- (1.44 + 7.84 + 0.64 + 0.04 + 4.84) / 5 = 14.8 / 5 = 2.96
Final Answer: The variance of the population of scores is 2.96.