Customer Service Chat
Get quote & make Payment
Tchebycheffs theorem, Statistics, Basic Statistics
As we all know standard deviation is a most widely used measure of variation. It has certain mathematical properties that facilitate development of statistical theory. It carries the same units as the variable, whereas the variable is expressed in squared units.
Deeper insight into the role and meaning of standard deviation can be gained through examination and use of a theorem developed by the Russian mathematician tchebycheff. According to this theorem, it is given a group of N within K standard deviations of the mean. The symbol K represents number of standard deviations. The theorem can be quantified for any desired value of K each different value of K produces a new interval with different minimum proportions of observations encompassed.
To illustrate, let K = 1, 2 and 3 when K = 1, this interval created is the mean ± 1 standard deviation, i.e. µ ± s. For this value of K the minimum proportion of observations contained in the interval is
1 + (1/K)^2 + 1 -1/1 = 1-1 = 0
When K = 2, the interval is µ ± 2s and the minimum proportion observation in the interval is:
1 – (1/)2 = 1 –1/4= 3/4.
When K = 3, interval is µ ± 3s and the minimum proportion of items in the interval is:
1 – (1/3)2 = 1 - 1/9 = 8/9
Posted Date: 1/31/2012 11:37:45 PM | Location : United States
Ask an Expert
Tchebycheffs theorem, Statistics, Assignment Help, Ask Question on Tchebycheffs theorem, Statistics, Get Answer, Expert's Help, Tchebycheffs theorem, Statistics Discussions
Write discussion on Tchebycheffs theorem, Statistics
Your posts are moderated
Write your message here..
What is cut-off date, What is cut-off date A chosen manually date whereby ...
What is cut-off date A chosen manually date whereby transactions usually are stopped to give for closing of the books of accounts for a known period: for audit purposes,
Define appraisal, Define appraisal (1) The act of evaluating. (2) The appr...
Define appraisal (1) The act of evaluating. (2) The approximated value as a result of such measures. Talk about APPRAISE
Corporate B onds/Preffered Stocks, If an exact answer isn''t possible, I re...
If an exact answer isn''t possible, I really just need a guide. The company we are using is GameStop Corp, listed as GME on the NYSE. Using the supplied information and referring
Is the coin biased, A coin that is balanced should come up heads half the t...
A coin that is balanced should come up heads half the time in the long run. A coin is tossed 4040 times and gives 2085 heads. Is the coin biased? Use Alpha = .05. (State the Hypoth
BUSINESS FORECASTING., a) What is analysis of variance? What are the assump...
a) What is analysis of variance? What are the assumptions of this technique? b) Three samples below have been obtained from normal populations with equal variances. Test the hypoth
Describe the assumptions conducting test, Conduct a test to determine if th...
Conduct a test to determine if the proportion of males that responded true to the statement in the survey that, "Whole foods (i.e. raw vegetables and meats) contain sodium," is dif
Eviews Task, I have one task to be done on Eviews.
I have one task to be done on Eviews.
ANOVA, This problem will introduce the learner into a technique called Anal...
This problem will introduce the learner into a technique called Analysis of Variance. For this course we will only conduct a simple One-Way ANOVA and touch briefly on the importan
Acceptance region, Acceptance Region A term related with the statistical...
Acceptance Region A term related with the statistical signi?cance tests, which provides the set of values of a test statistic for which the null hypothesis cannot rejected. Supp
Stat 2331 intro, Textbook The basic practice of statistics, 5th Edition b...
Textbook The basic practice of statistics, 5th Edition by David S. Moore; Freeman EX:14.37, 14.38, 14.39, 17.5, 17.28a
Accounting Assignment Help
Economics Assignment Help
Finance Assignment Help
Statistics Assignment Help
Physics Assignment Help
Chemistry Assignment Help
Math Assignment Help
Biology Assignment Help
English Assignment Help
Management Assignment Help
Engineering Assignment Help
Programming Assignment Help
Computer Science Assignment Help
Why Us ?
~24x7 hrs Support
~Quality of Work
~Time on Delivery
~Privacy of Work
Human Resource Management
Literature Review Writing Help
Follow Us |
T & C
Copyright by ExpertsMind IT Educational Pvt. Ltd.