How do you calculate the variance for a given set of population scores?

by

Understanding Variance

Variance is a statistical measurement that describes the spread of data points in a dataset. It indicates how much individual scores deviate from the mean (average) of the population. A higher variance means that data points are more spread out from the mean, while a lower variance indicates that they are clustered closely around the mean.

Steps to Calculate Variance

  1. Gather Your Data: First, list all the scores in your population. For example, let’s consider the following population scores: 5, 7, 3, 9, 4.
  2. Calculate the Mean: The mean (average) is calculated as follows:
    • Sum of scores: 5 + 7 + 3 + 9 + 4 = 28
    • Number of scores: 5
    • Mean: 28 / 5 = 5.6
  3. Determine the Deviations: Subtract the mean from each score to find the deviation of each score:
    • 5 - 5.6 = -0.6
    • 7 - 5.6 = 1.4
    • 3 - 5.6 = -2.6
    • 9 - 5.6 = 3.4
    • 4 - 5.6 = -1.6
  4. Square the Deviations: Square each of the deviations:
    • (-0.6)^2 = 0.36
    • (1.4)^2 = 1.96
    • (-2.6)^2 = 6.76
    • (3.4)^2 = 11.56
    • (-1.6)^2 = 2.56
  5. Calculate the Average of the Squared Deviations: Add these squared values, and then divide by the number of scores to find the variance:
    • Sum of squared deviations: 0.36 + 1.96 + 6.76 + 11.56 + 2.56 = 23.20
    • Variance: 23.20 / 5 = 4.64

The Result

The variance for the provided population of scores is 4.64. This value gives you an idea of how spread out the scores are around the mean. In summary, variance is a useful way to quantify the variability within your data.

Leave a Comment