standard deviation

standard deviation is defined for the given set of data in which data is spread or it is also called as data is distributed in the data set .It is defined for the distributed data set for defining the diversity of the set of data .standard deviation is the part of statistics in which we can understand that how data is deviated from its mean value or sometimes it will be denoted as the average value. You can also find the standard deviation for the given probability distribution.
According to definition of standard deviation which is given in cbse text books, it will used for finding the deviation of the data in the data set from the standard average value or mean value for that set of data .It will defined the dispersion of the data in form of variance that is sometimes called as the populated standard deviation .
sigma symbol (s) is used for specify the standard deviation and it is known as known as the standard deviation and there is one more way for defining the standard deviation that is square root of variance and it will be define as the (s 2) .
We can understand the standard deviation by specific expression that helps to understand the standard deviation very effectively:
If there in the data set a random variable (a) , for that mean value is define as m and it is denoted as in form of average or mean E | a | = m .
Where E denotes the average value of a .
so the formula for standard deviation is that is based on the mean value E is defined as
( s ) = √ E (a - m ) 2 .
Standard deviation is also expressed by formula of variance that is defined as square root of the variance and In the next session we will discuss about mode and you can also take chemistry tutoring from our website.

variance

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 ⁶_{i= 1}a_i / 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.