QQuestionStatistics
QuestionStatistics
What is the sample variance of the following numbers: 2, 4, 6, 8, 10, 12, 14?
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Answer
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Step 1:I'll solve this step-by-step using the sample variance formula:
Step 2:: Calculate the mean (average)
\bar{x} = \frac{2 + 4 + 6 + 8 + 10 + 12 + 14}{7} = \frac{56}{7} = 8
First, I'll sum all the numbers and divide by the total count:
Step 3:: Subtract the mean from each number and square the differences
\begin{aligned}
(2 - 8)^{2} &= (- 6)^{2} = 36 \ (4 - 8)^{2} &= (- 4)^{2} = 16 \ (6 - 8)^{2} &= (- 2)^{2} = 4 \ (8 - 8)^{2} &= 0^{2} = 0 \ (10 - 8)^{2} &= 2^{2} = 4 \ (12 - 8)^{2} &= 4^{2} = 16 \ (14 - 8)^{2} &= 6^{2} = 36 \end{aligned}
Step 4:: Sum the squared differences
\sum(x_{i} - \bar{x})^{2} = 36 + 16 + 4 + 0 + 4 + 16 + 36 = 112
Step 5:: Divide by (n- 1) to get sample variance
s^{2} = \frac{112}{7-1} = \frac{112}{6} = 20
Final Answer
The sample variance is 20.
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