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Chapter 18: Problem 690

If \(\mathrm{n}=100, \underline{\mathrm{x}}=3\) and \(\mathrm{S}^{2}=11\) then \(\left[\left(\sum \mathrm{xi}^{2}\right) /\left(\sum \mathrm{xi}\right)\right]\) is (a) 10 (b) 22 (c) \(6.66\) (d) 2000

Short Answer

Expert verified
(c) 6.66

Step by step solution

01

Calculate the sum of xi

\( \sum x_i = n \times x̄ = 100 \times 3 = 300 \) #Step 2: Calculate the sum of xi²# We are given the variance (S²), and we can use its formula to find the sum of xi². The formula for variance is: \( S^2 = \frac{ \sum x_i^2 - (\sum x_i)^2/n }{n-1} \) Now, we can find the sum of xi².
02

Rearrange the variance formula and solve for the sum of xi²

\( \sum x_i^2 = S^2 (n - 1) + \frac{(\sum x_i)^2}{n} \)
03

Plug in the values and calculate the sum of xi²

\( \sum x_i^2 = 11(100 - 1) + \frac{300^2}{100} = 11 \times 99 + 900 = 1089 + 900 = 1989 \) #Step 3: Calculate the value of [ (Σxi²) / (Σxi) ]# Now that we have the sum of xi and the sum of xi², we can calculate the required expression.
04

Calculate the value of [ (Σxi²) / (Σxi) ]

\(\left( \frac{\sum x_i^2}{\sum x_i} \right) = \frac{1989}{300} = 6.63\) Comparing this with the given options, we can see that the correct answer is approximately equal to 6.66. So, the answer is: (c) 6.66

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Most popular questions from this chapter

The value of the variable of the given data for which the number of observations with values less than it and grater than it are equal is (a) mean (b) median (c) mode (d) range

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