Bienayme-chebyshev rule, Applied Statistics

This probability rule determined by the research of the two mathematicians Bienayme' and Chebyshev, explains the variability of data about its mean when the distribution of the data set is not known. The rule states that the percentage of data observations lying within   1079_Bienayme-Chebyshev Rule1.png   standard deviations of the mean is at least

1387_Bienayme-Chebyshev Rule.png

 x 100

The above rule holds good regardless of the shape of the data set. The formula applies to differences greater than one standard deviation about the mean, and k being greater than 1.

If a particular random phenomenon follows the pattern of bell-shaped model which is usually a normal distribution, we precisely know how any element is likely to be closed to or far from its mean. But, if the population model is not known, the Bienayme' - Chebyshev rule applies. This rule tells how likely any particular value can lie within a specified distance from the mean. If a data set takes any shape, at least [1 - (1/2)2] 100 = 75% of the observations are contained within two standard deviations of the mean. In turn, at least 89% of all observations are contained within three standard deviations of the mean.

This rule helps managers to understand the information content of data when no known distribution can be assumed.

Rectangular distribution: It is used where every observation has the same frequency/probability. The inner rectangle contains at least 75% of the observations.

1048_rectangular distribution.png

Non-symmetrical distribution: When the two halves of a distribution about the mean are not mirror images of each other then it is termed as a non-symmetrical distribution. The shaded area below contains at least 75% of the observations.

1782_rectangular distribution1.png

Posted Date: 9/14/2012 4:05:41 AM | Location : United States







Related Discussions:- Bienayme-chebyshev rule, Assignment Help, Ask Question on Bienayme-chebyshev rule, Get Answer, Expert's Help, Bienayme-chebyshev rule Discussions

Write discussion on Bienayme-chebyshev rule
Your posts are moderated
Related Questions
Consider the following game: (a) If (top, left) is a Weakly Dominant Strategy Equilibrium, then what inequalities must hold among (a, ..., h)? (b) If (top, left) is a Na

Sample Standard Deviation So far, we discussed the population standard deviation. Now, let us switch to sample standard deviation(s) that is analogous to the population stand

The cost of living index number on a some data was 200. From the base period, the percentage enhances in prices were-Rent Rs 60, clothing Rs 250, Fuel and Light Rs 150 and Miscella

Multivariate analysis involves a set of techniques to analyse data sets on more than one variable. Many of these techniques are modern and often involve quite sophisticated use of

DISCUSS THE METHODS OF MEASURING TREND

find the expected value of the mean square error and of the mean square reggression

Calculation for Continuous Series or Grouped Data = where, m = mid-point of class   =

Type of Variable in Regression Analysis There are two types of variable in regression analysis. These are: a.      Dependent variable b.      Independent variable

The file Midterm  Data.xls has a tab labeled "National Grid vs. Alcoa" which presents historical price data for two stocks.  Using the National Grid price as the X-value and the Al

What is a null hypothesis? ..