Final answer:
To calculate the sample variance for the data set [6, 6, 8, 8, 8, 14, 6], we find the mean, calculate each data point's squared deviation from the mean, and average these squared deviations. The sample variance is found to be 14.
Step-by-step explanation:
The question is asking us to calculate the sample variance for the data set [6, 6, 8, 8, 8, 14, 6]. To compute this, we need to follow several steps which include finding the mean, calculating the squared deviations from the mean for each data point, and then determining the average of these squared deviations (± 1 since it is a sample and not a population).
- First, calculate the mean (average): (6+6+8+8+8+14+6)/7 = 56/7 = 8.
- Next, for each data value, subtract the mean and square the result: (6-8)² = 4, (8-8)² = 0, (14-8)² = 36, etc.
- Then sum these squared deviations: 4+4+4+0+0+0+36+36 = 84.
- Finally, divide by the number of data points minus one (n-1) which is 6 in this case: 84/6 = 14.
The sample variance is 14, which is already to one decimal point as required.