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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 standard deviations of the mean is at least
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.
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.
(1) What values can the response variable Y take in logistic regression, and hence what statistical distribution does Y follow? The response variable can take the value of either
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Now, let's look at a different linear combination. Suppose we are interested n comparing the average mean log income for no college education ( 16). 1. Write out the linear com
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For calculating the mode of the grouped data graphically, the following procedure is adopted. Draw a histogram of the data; the modal class is the tallest rectangle.
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a b c d e supply p 3 4 6 8 8 20 q 2 6 0 5 8 30 r 7 11 20 40 3 15 s 1 0 9 14 6 13 d 15 3 12 10 20
"index number is an economic barometer" comment on this statement
The first step in this case is to ensure that you are adequately clear on the General Linear Model and its relationship to both ANOVA and regression. The distinction is approxim
Histogram: It is generally used for charting continuous frequency distribution. In histogram, data are plotted as a series of rectangle one over the other. Class intervals
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