Final answer:
The sample variance of the data set [8,8,6,8,7,8,6,6,9,7] is calculated by finding the mean, determining the squared deviations from the mean, summing those squared deviations, and dividing by the number of data values minus one, resulting in a sample variance of approximately 1.5222.
Step-by-step explanation:
To compute the sample variance of the data set [8,8,6,8,7,8,6,6,9,7], first calculate the mean of the data. The mean (average) is found by summing all the data values and dividing by the number of values. For this set, the mean is (8+8+6+8+7+8+6+6+9+7)/10 = 73/10 = 7.3.
Next, subtract the mean from each data value and square the result to find the squared deviations. Then, sum all the squared deviations. Finally, divide this sum by the number of data values minus one to obtain the sample variance.
Let's perform these steps:
- Squared deviations: (8-7.3)^2, (8-7.3)^2, (6-7.3)^2, (8-7.3)^2, (7-7.3)^2, (8-7.3)^2, (6-7.3)^2, (6-7.3)^2, (9-7.3)^2, (7-7.3)^2
- Sum of squared deviations: 0.49+0.49+1.69+0.49+ ... +2.89+0.09
- Sum of squared deviations (total): 13.7
- Sample variance: 13.7/(10-1)
- Sample variance: 13.7/9 = 1.5222
The sample variance for this data is approximately 1.5222.