Final answer:
To find the variance of the data set {10, 19, 21, 28, 12, 20, 16}, calculate the mean, find the squared deviations from the mean, sum the squared deviations, and divide by the count minus one. The sample variance is approximately 36.33.
Step-by-step explanation:
To calculate the variance for the data set {10, 19, 21, 28, 12, 20, 16}, follow these steps:
1. Find the mean of the data set by adding all the numbers together and then dividing by the count of numbers. Mean = (10 + 19 + 21 + 28 + 12 + 20 + 16) / 7 = 126 / 7 = 18.
2. Subtract the mean from each data point to find the deviations, then square each deviation to find the squared deviations.
3. Calculate the sum of the squared deviations. Σ(x - mean)² = (10 - 18)² + (19 - 18)² + (21 - 18)² + (28 - 18)² + (12 - 18)² + (20 - 18)² + (16 - 18)² = 64 + 1 + 9 + 100 + 36 + 4 + 4 = 218.
4. Divide the sum of the squared deviations by the count of numbers minus one, which is 6 in this case, to obtain the sample variance. Variance s² = 218 / 6 ≈ 36.33
The sample variance for the given data set is approximately 36.33, rounded to the nearest hundredth.