Tchebycheffs theorem, Statistics, Basic Statistics

Tchebycheffs theorem

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







Related Discussions:- 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
Related Questions
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 (1) The act of evaluating. (2) The approximated value as a result of such measures. Talk about APPRAISE

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

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

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

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

I have one task to be done on Eviews.

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 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

Textbook The basic practice of statistics, 5th Edition by David S. Moore; Freeman EX:14.37, 14.38, 14.39, 17.5, 17.28a