Previously we have discussed about verifying trigonometric identities and In today's session we are going to discuss about variance which comes under board of intermediate education andhra pradesh syllabus, In statistics (statistics tutor), Variance is used for measurement between the data of a data set and its mean value. Sometimes it is defined as the moment of the distribution. It is also used in the probability distribution for distinguish it and it is expressed as the parameter that describe the probability distribution for every situation.
Variance is defined as the square of the standard deviation that is denoted by the symbol sigma (s) and variance is shown as (s)2.
Variance is the measure of the farness of the data in the given data set from its mean value .so variance is based on the mean value of the data set and also defined in the expression as for a given data set standard deviation is define the distribution .
In a given data set for any random variable ‘x’, mean value is define as ‘m’ and it is denoted as E |x| = mand here ‘E’ denotes the average value of random variable ‘x’.
Here formula for variance is defined as (s)2= E (x - m)2.
So, formula for standard deviation is square root of variance (s) = √ E (x - m )2.
Here in above expression (s)defines the Standard deviation by the square root of the variance of random variable ‘x’ or if we have the value of standard deviation and we want to calculate the variance that is define as the square of the standard deviation as s2.
If there are a given data set as there defines the variable as:
Variable: a1 a2 a3 a4 a5 a6
Value: 3 4 4 5 6 8
Then find the variance?
So, mean m = å 6i= 1ai / n = 30 / 6 = 5,
Variance as s2= å (x - m )2/ n.
By using formula we calculate the value of variance s2 = 2.67.
In the next session we will discuss about standard deviation.
Variance is defined as the square of the standard deviation that is denoted by the symbol sigma (s) and variance is shown as (s)2.
Variance is the measure of the farness of the data in the given data set from its mean value .so variance is based on the mean value of the data set and also defined in the expression as for a given data set standard deviation is define the distribution .
In a given data set for any random variable ‘x’, mean value is define as ‘m’ and it is denoted as E |x| = mand here ‘E’ denotes the average value of random variable ‘x’.
Here formula for variance is defined as (s)2= E (x - m)2.
So, formula for standard deviation is square root of variance (s) = √ E (x - m )2.
Here in above expression (s)defines the Standard deviation by the square root of the variance of random variable ‘x’ or if we have the value of standard deviation and we want to calculate the variance that is define as the square of the standard deviation as s2.
If there are a given data set as there defines the variable as:
Variable: a1 a2 a3 a4 a5 a6
Value: 3 4 4 5 6 8
Then find the variance?
So, mean m = å 6i= 1ai / n = 30 / 6 = 5,
Variance as s2= å (x - m )2/ n.
By using formula we calculate the value of variance s2 = 2.67.
In the next session we will discuss about standard deviation.
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