Final answer:
To calculate the sample variance of the dataset 1, 6, 7, 3, 5, 2, first find the mean, then compute the sum of the squared differences from the mean, and finally divide by the number of values minus one. The sample variance is 5.6.
Step-by-step explanation:
To calculate the sample variance for the dataset 1, 6, 7, 3, 5, 2, we first need to find the mean of the dataset. Add all the numbers together and divide by the number of values in the dataset (n).
Mean (\(\bar{x}\)) = (1 + 6 + 7 + 3 + 5 + 2) / 6 = 24 / 6 = 4.
Next, subtract the mean from each data value, square the result, and sum these squared differences.
- (1 - 4)^2 = 9
- (6 - 4)^2 = 4
- (7 - 4)^2 = 9
- (3 - 4)^2 = 1
- (5 - 4)^2 = 1
- (2 - 4)^2 = 4
The sum of the squared differences is 9 + 4 + 9 + 1 + 1 + 4 = 28.
To find the sample variance (s^2), we divide this sum by n - 1 (which is 6 - 1 = 5) because we're dealing with a sample, not a population.
Sample variance (s^2) = 28 / 5 = 5.6
Therefore, the sample variance of the dataset is 5.6.