Tag: business economics and quantitative methods

Variance is the mean of the squares of the deviations from the mean. Variance is not affected by the addition, subtraction, multiplication and division of the given value. Therefore, if each value of the series is multiplied by 15, the coefficient of variation will be unaltered.

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data. Standard deviation is not affected by the increase of decrease of observations in the series. 

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Standard deviation = { (sum of the squares of the observations/ number of observations ) – (sum of observations/ number of observations ) } ^½

                               = { (1444) –(18.4) } ^½

                                = (1425.6) ^½

                                = 37.75 

Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.

Coefficient of variation = ( standard deviation / mean )x 100 

                                     = ( 37.75/ 18.4)x100

                                     = 20.51 

In probability two events are said to be independent if the occurrence of one event is not affected by the occurrence of another event. Both the variable are completely independent of each other. These events are also known as mutually exclusive event as they have no common point. 

• Mean deviation is the arithmetic average of the deviations of the observed values from an  average of the observed values. Since Mean deviation do not include negative value of the deviations. Therefore, it does not follow the algebraic value of the deviations.
  
• Range is defined as the difference between the highest(or largest ) and lowest(or smallest) observed value in a series. It is the most simple and commonly understandable measures of dispersion. Since it is the most affected measures of dispersion by the extreme values of the series, it is regarded as the crudest measure. 
  
• Coefficient of variation is the coefficient of dispersion based on the standard deviation of the statistical series.Therefore, Coefficient of variation is a unit less or relative measure of dispersion as variation is the absolute measure of dispersion. 
  

Standard deviation is the square root of the arithmetic mean of the squares of the deviations measured from the arithmetic mean of the data.

Variance is the mean of the squares of the deviations from the mean. 

Standard deviation is the square root of variance or variance is the square of standard deviation. 

S.D = {Var(X)}^1/2 

or 

Var(X) = (S.D)²

A frequency distribution is a tabular summary of data showing the frequency of items in each of several non-overlapping classes. It organizes raw data into a structured table format.

Given N=100, old mean=40, old SD=5.1. The sum of observations is S_old = 100 * 40 = 4000. Correct sum = 4000 - 50 + 40 = 3990, so correct mean = 3990 / 100 = 39.9. For the standard deviation, old sum of squares (SS) can be found using SD^2 = (SS/N) - mean^2, yielding SS_old = 100 * (5.1^2 + 40^2) = 162601. Correct SS = 162601 - 50^2 + 40^2 = 161701. Correct variance = (161701 / 100) - (39.9^2) = 1617.01 - 1592.01 = 25, giving correct SD = sqrt(25) = 5.

The formula for covariance is Cov(x,y) = r * SD(x) * SD(y). Plugging in the values: 35 = 0.7 * 5 * SD(y). Thus, 35 = 3.5 * SD(y), which means SD(y) = 35 / 3.5 = 10.