Log out Go to App
Go to App

Learning Materials

Features

Discover

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

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

For three events \(A, B, C\) \(P(\) exactly one of \(A\) or \(B\) occur \()=P\) \(P(\) exactly one of \(B\) or \(C\) occur \()=P\) \(P(\) exactly one of \(C\) or \(A\) occur \()=P\) And \(P(\) all three occur \()=P^{2} .\) Where \(0

For 100 observations \(\sum(x i-30)=0\) and \(\sum(x i-30)^{2}=10000\) then C.V. (coefficient of variance) is \(\%\) (a) 10 (b) 100 (c) \(33.33\) (d) 30

Find mean and S.D. from given data $$ \begin{array}{|l|c|c|c|c|c|} \hline \text { Class } & 33-35 & 36-38 & 39-41 & 42-44 & 45-47 \\ \hline \text { Frequency } \mathrm{f} & 17 & 19 & 23 & 21 & 20 \\ \hline \end{array} $$ (a) \(40.24,4.20\) (b) \(40.24,4.30\) (c) \(4.5,40.20\) (d) \(40.24,4.90\)

Out of 3 n consecutive integers three are selected at random the probability that there sum is divisible by 3 is (a) \(\left[\left(3 n^{2}-n-2\right) /\\{(3 n-1)(3 n-2)\\}\right]\) (b) \(\left[\left(n^{2}-3 n+2\right) /\\{(3 n-1)(3 n-2)\\}\right]\) (c) \(\left[\left(3 n^{2}-3 n+2\right) /\\{(3 n-2)(3 n-3)\\}\right]\) (d) \(\left[\left(3 n^{2}-3 n+2\right) /\\{(3 n-1)(3 n-2)\\}\right]\)

For a data there are 3n observations in which first \(n\) observations are \(a-d\), second n observation are a and last n observations are \(a+d\) and there variance is \((4 / 3)\) then \(|\mathrm{d}|=\) (a) 1 (b) \(\sqrt{2}\) (c) \(\sqrt{(2 / 3)}\) (d) \(\sqrt{(3 / 2)}\)
See all solutions

Recommended explanations on English Textbooks

Essay Plan

Read Explanation

Lexis and Semantics

Read Explanation

English Grammar Summary

Read Explanation

Syntax

Read Explanation

Linguistic Terms

Read Explanation

Argumentative Essay

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free