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.

Permutations and combinations

Hello students, in this blog we are going to discuss the topic of permutations and combinations. These two topics are extensively used in mathematics.
Permutations: - The different arrangement of a given number of things by taking some or all at a time, are called the permutations. Let’s take a close look on the permutations.
All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking two at a time are (ab, ba, ac, ca, bc, cb).
 All permutations made with the letter ‘a’, ‘b’, ‘c’ by taking all at a time are (abc, acb, bac, bca, cab, cba).
Combinations: As name suggest of the combination that it is concept in which every number of separate groups are made by the when we include few or all number of an object, then it is known as the combination.
Suppose we want to select two out of three boys A, B, C. Then possible selections are AB, BC and CA.
Note that AB and BA represent the same selections.
Formula for permutation and combination are:
For permutation: “P r = n (n - 1) (n - 2)……(n –r + 1) = n! / (n - r) !,
Example for this: 1. 6 p2 =(6 * 5) = 30.                  2. 7 P 3 = (7 * 6 * 5) = 210.
 For combination: “C r = n ! / (r !) (n - r) ! = (n - 1) (n - 2)……to r factors / r !,
Example. ¹¹ C ₄ = (11 * 10 * 9 * 8) / (4 * 3 * 2 * 1) = 330, (know more about icse board papers, here)
So applying both the formulas we can solve any permutation and combination problems.
In the next session we will discuss about Types of events.