Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 18: Problem 752

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

Short Answer

Expert verified
The coefficient of variation (C.V.) is \(33.33\%\).

Step by step solution

01

Find the mean (µ)

Since we know that \(\sum(x_i - 30) = 0\), we can write this as \(\sum x_i - \sum 30 = 0\) Now, since there are 100 observations, \(\sum 30 = 30\times 100\), which means \(\sum x_i - 3000 = 0\) So, the sum of all x_i is \(\sum x_i = 3000\) Now, we can find the mean as follows: \(\mu = \frac{\sum x_i}{n}\) Where n is the number of observations (100 in this case). \(\mu = \frac{3000}{100} = 30\).
02

Find the variance (σ^2)

We have given that \(\sum(x_i - 30)^2 = 10000\). Now, let's find the variance, σ^2. Variance, σ^2 is defined as: \(\sigma^2 = \frac{\sum(x_i - \mu)^2}{n}\) We know that: - n = 100 (number of observations) - µ = 30 (mean of the dataset) Substituting the values: \(\sigma^2 = \frac{10000}{100} = 100\)
03

Find the standard deviation (σ)

To find the standard deviation (σ), we need to find the square root of the variance (σ^2). \(\sigma = \sqrt{100} = 10\)
04

Compute the Coefficient of Variation (C.V.)

Now that we have both the mean (µ) and standard deviation (σ), we can calculate the coefficient of variation (C.V.) as follows: C.V. = \(\frac{\sigma}{\mu} \times 100\%\) C.V. = \(\frac{10}{30} \times 100\%\) C.V. = \(33.33 \%\) So, the correct answer is (c) \(33.33\%\).

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

The sum of the squares of deviation for 10 observations taken from their mean 30 is 90 . The coefficient of variation is (a) \(20 \%\) (b) \(10 \%\) (c) \(11 \%\) (d) \(12 \%\)

The weighted mean of first \(n\). natural numbers whose weights are equal to the squares of corresponding numbers is (a) \([(n+1) / 2]\) (b) \([\\{3 n(n+1)\\} /\\{2(2 n+1)\\}]\) (c) \([\\{(n+1)(2 n+1)\\} / 6]\) (d) \([\\{n(n+1)\\} / 2]\)

Using \(1,2,3,4,5,6\) four digit numbers without repetition of any digit are formed. If one number is taken from these what is the probability that the selected number is divisible by \(4 ?\) (a) \((96 / 6 !)\) (b) \(\left(96 /{ }^{6} \mathrm{P}_{4}\right)\) (c) \(\left(84 /{ }^{6} \mathrm{P}_{4}\right)\) (d) None

In a series of \(2 \mathrm{~m}\) observations half of them equal to \(\mathrm{b}\) and remaining half equal to \(-b\). If the standard deviation of the observations is 3 then \(|\mathrm{b}|=\) (a) 3 (b) \(\sqrt{3}\) (c) \((\sqrt{3} / \mathrm{n})\) (d) \((1 / \mathrm{n})\)

A student obtain \(75 \%, 80 \%\) and \(85 \%\) in three subjects. If the marks of another subject are added then his average cannot be less then (a) \(60 \%\) (b) \(65 \%\) (c) \(80 \%\) (d) \(90 \%\)
See all solutions

Recommended explanations on English Textbooks

Listening and Speaking

Read Explanation

Argumentative Essay

Read Explanation

5 Paragraph Essay

Read Explanation

Sociolinguistics

Read Explanation

Blog

Read Explanation

Syntax

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