Final answer:
To find the sample variance, compute the mean, subtract each number from the mean, square the result, sum these squared differences, and divide by one less than the sample size. The calculated variance does not match the provided options, but the closest answer would be B. 94.33, although the actual variance differs.
Step-by-step explanation:
To calculate the sample variance for the set of numbers (150, 142, 128, 123, 127, 134), we first need to find the mean of the sample:
- Add up all the numbers: 150 + 142 + 128 + 123 + 127 + 134 = 804.
- Divide the sum by the number of items in the sample: 804 / 6 = 134.
This is the mean of the sample.
Next, we find the squared difference from the mean for each number, sum them, and then divide by the number of items minus one to get the sample variance:
- (150 - 134)^2 + (142 - 134)^2 + ... + (134 - 134)^2 = 256 + 64 + ... + 0 = 568.
- Divide this sum by the number of items minus 1: 568 / (6 - 1) = 113.6.
The sample variance is therefore 113.6, which is not one of the options provided, indicating a potential mistake in the calculation or the options given. However, based on the provided context, we can calculate the variance using the correct method.
To correct this, let's re-calculate the squared differences (as a step was missed in the variance calculation previously), which are:
- (150 - 134)^2 = 256
- (142 - 134)^2 = 64
- (128 - 134)^2 = 36
- (123 - 134)^2 = 121
- (127 - 134)^2 = 49
- (134 - 134)^2 = 0
The sum of these squared differences is 256 + 64 + 36 + 121 + 49 + 0 = 526.
Now, divide this sum by the sample size minus one (n-1) to get the sample variance: 526 / (6 - 1) = 526 / 5 = 105.2.
Please note that this result still does not match the multiple-choice options provided, suggesting either a misunderstanding in the process or an error in the question itself. Given the options, the closest answer to the calculated variance is B. 94.33, but with an explanation that the actual calculated variance differs.