Mean Variance Theory

In mathematics, it includes various chapters like geometry, statistics, number systems, probability, algebra, etc. Statistics is one of the important chapters in math. It deals with the terms mean, variance, mode, standard deviation, etc. Mean is used to calculate the average of a given set of numbers. Variance is also one of the important terms of statistics. Here we see about the mean variance theory.

I like to share this Variance Calculator with you all through my article.

Definitions and Formulas in Mean Variance Theory:

Mean:

It is a mathematical term in the chapter statistics in which it is defined as the total average of a group of numbers. It is found or calculated by adding all the numbers in a given set and divide the sum by number of given values.

Formula:

The formula for mean is derived as,

Mean  = (a_1+a_2+............a_n)/n

Where,

a_1+ a_2+..........a_n = sum of numbers

n is the total numbers given.

This is the formula for mean.

Variance:

It is also one of the mathematical terms of statistics. It is defined as the descriptor or a parameter of the theoretical probability distribution.

Formula for variance:

The term variance is found out by taking square root of standard deviation. Hence it depends on the term standard deviation.

Standard deviation = sqrt((sum d^2)/n)

Here, d is calculated by (x -barx)

barx is the mean value and x is the given values.

n is the number of given values.

These are involved in mean variance theory.

I am planning to write more post on Triangle Inequality Proof and X and y Intercept. Keep checking my blog.

Problem for Mean Variance Theory:

Calculate the mean and variance for a sequence of 60, 50. 40, 90, 95.

Solution:

1. Mean:

First we have to arrange the given numbers in ascending order. That is, 40, 50, 60, 90, 95.

Add all the values and then divide by total given numbers.

Mean = (40+ 50+ 60+ 90+ 95)/5

= 335/5

Therefore the mean barx = 67

2. Variance:

To find we have to find standard deviation.

We have Standard deviation =  sqrt((sum d^2)/n) .
x x - barx
(x - barx ) 2
60 -7 49
50 -17 289
40 -27 729
90 23 529
95 28 784


Here, we find sum d^2

Substitute in formula,

Now standard deviation =sqrt((sumd^2)/n)  = sqrt(2380/5) = 21.817.

Variance = sqrt(21.817) = 4.67

Hence the variance is calculated as 4.67.

Thus these are involved in mean variance theory.