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

Normal probability plots, The Null Hypothesis - H0:  The random errors will...

The Null Hypothesis - H0:  The random errors will be normally distributed The Alternative Hypothesis - H1:  The random errors are not normally distributed Reject H0: when P-v

Cartogram or mapograph, Cartogram or Mapograph:   Statistical maps are a...

Cartogram or Mapograph:   Statistical maps are also used to represent data like density of population indifferent states in the country or different countries in the world or th

Use of calculators in statistics, In recent years a number of calculators a...

In recent years a number of calculators are available for doing statistical calculations over and above the usual addition, subtraction, multiplication and division. The fx-82 mode

Research tool, what are the characteristics of research tool?

what are the characteristics of research tool?

Frequency distribution, Frequency distribution A frequency distribution...

Frequency distribution A frequency distribution is a series where a number of items with similar values are put in separate groups or bunches. In other words a frequency distri

Compute the sample mean and sample standard deviation, We want to investiga...

We want to investigate the income data.  In the Excel file Midterm  Data.xls there is a tab labeled "Income Data 2006".  The data in the tab is the income reported by 400 people in

Evaluate gross reproduction rate, Evaluate Gross Reproduction Rate: Fr...

Evaluate Gross Reproduction Rate: From the data given below compute : i)   General  Fertility  Rate ii)  Specific  Fertility  Rate iii)  Total  Fertility  Rate iv)

Standard error, Standard Error The measure of reliability of the estima...

Standard Error The measure of reliability of the estimating equation that we have developed is given by standard error of estimate. The standard error of estimate represented b

Calculate the seasonal indexes , The total number of overtime hours (in 100...

The total number of overtime hours (in 1000s) worked in a large steel mill was recorded for 16 quarters, as shown below. Year Quarter Overtime hour

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