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

Weibull distribution, slope parameter of 1.4 and scale parameter of 550.cal...

slope parameter of 1.4 and scale parameter of 550.calculate Reliability, MTTF, Variance, Design life for R of 95%

Correlation coefficient, Consider three stocks A, B and C costing $100 each...

Consider three stocks A, B and C costing $100 each. The annual returns on the three stocks have mean $5 and variance $10. a. Suppose that the returns on the three stocks are i.i

Probability and expectation, Ten balls are put in 6 slots at random.Then ex...

Ten balls are put in 6 slots at random.Then expected total number of balls in the two extreme slots

Recitilinear motion, velocity of a particle which moves along the s-axis is...

velocity of a particle which moves along the s-axis is given by v=2-4t+5t then find position velocity,acceleration

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

Simulation, Simulation When decisions are to be taken under conditions ...

Simulation When decisions are to be taken under conditions of uncertainty, simulation can be used. Simulation as a quantitative method requires the setting up of a mathematical

Types of averages, The following are the various types of common averages u...

The following are the various types of common averages used in statistical analysis given in the form of a chart. Figure 1

The weekly treatment , A researcher is interested in comparing the effectiv...

A researcher is interested in comparing the effectiveness of three different parts of therapy for anger problems. 8 participants are randomly assigned to 3 treatment conditions: Co

Agreement, Agreement The degree to which different observers, raters or ...

Agreement The degree to which different observers, raters or diagnostic the tests agree on the binary classification. Measures of agreement like that of the kappa coefficient qu

Statistical procedures - estimation of a mean, Old Faithful Geyser in Yello...

Old Faithful Geyser in Yellowstone National Park derives its names and fame from the regularity (and beauty) of its eruptions. Rangers usually post the predicted times of eruptions

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