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Find the Variance of the following data:{6},{8},{10},{12},{14}

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Find the Variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$

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Find the Variance of the following data:

6, 8, 10, 12, 14, 16, 18, 20, 22, 24

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Text solutionVerified

Solution: Variance

= σ^{2} = i \sum n \frac{( x _{i} - x ) ^{2}}{n}

Here, n = no. of terms = 10Now,

\overline{x} = M e a n = \frac{\sum x}{n} = \frac{6 + 8 + 10 + 12 + 14 + 16 + 18 + 20 + 22 + 24}{10} = \frac{150}{10} = 15

∴ M e a n = 15

σ^{2} = \frac{1}{10} ((- 9)^{2} + (- 7)^{2} + (- 5)^{2} + (- 3)^{2} + (- 1)^{2} + 1^{2} + 3^{2} + 5^{2} + 7^{2} + 9^{2})

= \frac{2}{10} (81 + 49 + 25 + 9 + 1)

= \frac{1}{5} (165)

= 33

∴ V a r i a n c e = 33

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Question Text	Find the Variance of the following data: $6, 8, 10, 12, 14, 16, 18, 20, 22, 24$
Answer Type	Text solution:1
Upvotes	150