Bienayme-chebyshev rule, Applied Statistics

Assignment Help:

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


Related Discussions:- Bienayme-chebyshev rule

Asymmetric proximity matrices, Asymmetric proximity matrices Immediacy...

Asymmetric proximity matrices Immediacy matrices in which the off-diagonal elements which are, in the i th row and j th column and the j th row and i th column, are not essent

Correlation, Definition of Correlation According  to prof, king correla...

Definition of Correlation According  to prof, king correlation means that between two series or group  of data  there  exists  some casual connection  prof, king  has also  exp

Find the conditional distribution of turning diameter, 1. Assume the random...

1. Assume the random vector (Trunk Space, Length, Turning diameter) of Japanese car is normally distributed and the unbiased estimators for its mean and variance are the truth. For

Estimate the standard deviation of the process, Estimate the standard devia...

Estimate the standard deviation of the process: Draw the X (bar) and R charts for the data given and give your comments about the process under study. Estimate the standard de

Types of sampling, Given a certain population there are various ways in whi...

Given a certain population there are various ways in which a sample may be drawn from it. The chart below illustrates this point: Figure 1 In  Judgem

Calculation for discrete series or ungrouped data , Calculation for Discre...

Calculation for Discrete Series or Ungrouped Data The formula for computing mean is = where,          f  = fr

Demand, A monopolist firm''s demand curve is given by P:100-2q. (a) Find it...

A monopolist firm''s demand curve is given by P:100-2q. (a) Find its marginal revenue function.

Find the relation between two substance, Find the Relation between two subs...

Find the Relation between two substance: The following table shows the results obtained in experiments aimed to determine how solubility of water in benzene depends on tempera

Regression model, Using a random sample of 670 individuals for the populati...

Using a random sample of 670 individuals for the population of people in the workforce in 1976, we want to estimate the impact of education on wages. Let wage denote hourly wage in

Cluster sampling, Cluster Sampling This method is also known as multi s...

Cluster Sampling This method is also known as multi stage sampling .Under this method random selection is made of the ultimate or final units from a given stratum. The sampling

Write Your Message!

Captcha
Free Assignment Quote

Assured A++ Grade

Get guaranteed satisfaction & time on delivery in every assignment order you paid with us! We ensure premium quality solution document along with free turntin report!

All rights reserved! Copyrights ©2019-2020 ExpertsMind IT Educational Pvt Ltd