Properties of standard deviation, Applied Statistics

Assignment Help:

PROPERTIES

 

1. The value of standard deviation remains the same if, in a series each of the observation is increased or decreased by a constant quantity. In statistical language, we say standard deviation is independent of change of origin.

         For example, for the observations 3, 10 and 12 then μ = 8.33 and σ= 3.859.

If we increase the value of each observation by 4.5, we get the observations 7.5, 14.5 and 16.5.

         Now,  μ   = 12.833 and  σ = 3.859

         Hence although  μ  has increased by 4.5,  σ  remains the same.

2. For a given series, if each observation is multiplied or divided by a constant quantity, standard deviation will also be similarly affected.

Consider the observations 3, 10, 12.  σ  = 3.859 as shown in the above calculation.

Suppose we multiply each observation by 6, the observations become 18, 60 and 72.

  μ   =  50

σ

= 1353_properties of standard deviation.png
  = 23.152

  Which is nothing but the earlier  σ , 3.859 x 6.

In short, standard deviation is independent of any change of origin, but dependent on the change of scale.

3. Standard deviation is the minimum root-mean-square deviation. In other words, the sum of the squares of the deviations of items of any series from a value other than the arithmetic mean would always be greater.

4. Just as it is possible to compute combined mean of two or more groups, it is also possible to compute combined standard deviation of two or more groups. Combined standard deviation denoted by  σ12 is computed as follows:

σ12

= 1001_properties of standard deviation1.png

where,

μ1

=  Mean of first group

μ2

= Mean of second group

σ1

= Standard deviation of first group

σ2

= Standard deviation of second group

N1 

Number of observations in the first group

N2

= Number of observations in the second group

d1

= μ1 -  μ

d2

= μ2 -  μ

μ

 = (N1  μ1 + N2 μ2 ) / (N1 + N2)

Related Discussions:- Properties of standard deviation

Coefficient of determination, Coefficient of Determination The c...

Coefficient of Determination The coefficient of determination is given by r 2 i.e., the square of the correlation coefficient. It explains to what extent the variation

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

Bienayme-chebyshev rule, This probability rule determined by the research o...

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 dat

Probability theory, Origin and Development of probability Theory: The c...

Origin and Development of probability Theory: The credit for origin and development of probability goes to the European gamblers of 17 th century. They  used to gamble  on gam

Inverse cumulative distribution function, The Null Hypothesis - H0: β0 = ...

The Null Hypothesis - H0: β0 = 0, H0: β 1 = 0, H0: β 2 = 0, Β i = 0 The Alternative Hypothesis - H1: β0 ≠ 0, H0: β 1 ≠ 0, H0: β 2 ≠ 0, Β i ≠ 0      i =0, 1, 2, 3

Financial payments technology, Suppose the money supply process is now repr...

Suppose the money supply process is now represented by the following function: where m measures the sensitivity of money supply with respect to the interest rate. (i) Us

Limitations of arithmetic mean, The calculations of arithmetic mean m...

The calculations of arithmetic mean may be simple and foolproof, but the application of the result may not be so foolproof. An arithmetic mean may not merely lack

Production took place, Scenario: To fundraise for middle school camp the ye...

Scenario: To fundraise for middle school camp the year 3 and 4 syndicate designed and produced chocolate treats to sell to the year 1 and 2, and year 5 and 6 students at morning te

Probability, .1 Modern hotels and certain establishments make use of an ele...

.1 Modern hotels and certain establishments make use of an electronic door lock system. To open a door an electronic card is inserted into a slot. A green light indicates that the

Perform a simple linear regression analysis, In New Jersey, banks have been...

In New Jersey, banks have been charged with withdrawing from counties having a high percentage of minorities. To substantiate this charge, data is presented in the table below conc

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