Final answer:
To find the sample variance of the data set 6, 12, 11, 11, first calculate the mean, then the squared deviations from the mean, sum them up, and divide by the number of data points minus one. The sample variance is approximately 7.33.
Step-by-step explanation:
To calculate the sample variance of the data set 6, 12, 11, 11, we first need to find the mean (average) of these numbers. The mean is (6 + 12 + 11 + 11) / 4 = 40 / 4 = 10. Now we find the deviation of each number from the mean, square each of these deviations, and sum them up. The squared deviations are (6 - 10)^2 = 16, (12 - 10)^2 = 4, (11 - 10)^2 = 1, and (11 - 10)^2 = 1. So, their sum is 16 + 4 + 1 + 1 = 22.
The sample variance is calculated by dividing this sum by the number of data points minus one (n - 1). In this case, n = 4, so n - 1 = 3. Therefore, the sample variance is 22 / 3, which equals approximately 7.33. This represents the variability of the data set around the mean.