Final answer:
To find the sample variance, subtract the mean from each data value, square the result, add up all the squared differences, and divide by (n - 1). The sample standard deviation is the square root of the sample variance.
Step-by-step explanation:
To find the sample variance and standard deviation, follow these steps:
- Find the mean of the data set: (19 + 12 + 6 + 8 + 9) / 5 = 10.8
- Subtract the mean from each data value and square the result:
- (19 - 10.8)^2 = 72.36
- (12 - 10.8)^2 = 1.44
- (6 - 10.8)^2 = 18.36
- (8 - 10.8)^2 = 8.64
- (9 - 10.8)^2 = 3.24
Add up all the squared differences: 72.36 + 1.44 + 18.36 + 8.64 + 3.24 = 104.04Divide the sum by (n - 1), where n is the number of data values (5 - 1): 104.04 / 4 = 26.01The sample variance is 26.01To find the sample standard deviation, take the square root of the sample variance: sqrt(26.01) = 5.1