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# Measurability And Variability

If we are performing operation on any statically data it many happen that we obtain result after performing two operations. Then it can happen that we get two different results for the same data then it is called as Statistics variability. Variability statistics definition can be described as the variation in distribution from its Mean. If there will be a distribution which is lacking in variability statistics then it is called as homogeneous. There are three measures of variability, Range, standard deviation and variance of proportion. Firstly we will discuss range
Range of any data is the difference between the highest Point and lowest point. If we are having a data as 8, 5, 6, 2 then The Range will be 8 - 2 = 6. So the required range will be 6. Now we will move to variance of proportion,
If we talk about any population then variance of proportion is the average Square deviation from the mean of the population, we can find the variance with the help of formula given below,
σ2 = Σ (Xi - μ)2 / N,
Here σ2 is the variance of population; ‘μ’ is the mean of the population, ‘n’ is the number of element in the population and ‘Xi’ is the ith element of the sample.
Now we will discuss about the Standard Deviation,
We can find standard deviation of any population with the help of variance; if we do the square root of variance we will get the standard deviation. The formula for the standard deviation is given below,
σ = sqrt Σ ( Xi - μ )2 / N,
Here ‘σ’ is the standard deviation of population; ‘μ’ is the mean of the population, ‘n’ is the number of element in the population and ‘Xi’ is the ith element of the sample.
This is all about the three measures of variability.

## The Range

Smallest Interval length containing all Set of data is called as Range. It can be calculated by finding the smallest and greatest observations and then subtracting them. Units of the Statistics range is same as of the data. Its calculation is dependent on two sample observations, so it is considered as Weak Measurement of the Statistics specially when the sample size is large....Read More

## Variance of a Random Variable

Random variables are the variables which we will get after the experiment, that variable can be any numeric value. We always get a specific value after the experiment if this value is fixed then experiment is called as Random Variable and if it is not then it is called infinite random variable. For finding variance we need to find the Standard Deviation fir...Read More

## Standard Deviation of a Random Variable

We can define Random Variable as; if ‘X’ is a random variable and we are doing any experiment then we can assign any value to ‘X’ which we are getting from the given experiment. We are here to discuss about Standard Deviation of a Random Variable, before studying that we should have a good knowledge of random variable so we will discuss that in de...Read More

## Statistics Notations

Mathematical objects and ideas are represented by the notation or in other word we can say that it is system of symbolic representation of many ideas and many objects. It also includes the relatively symbolic representation. Such as the number i.e. 0, 1, 2, it also include function symbols such as sin and +. Conceptual symbol also included in the notation such as limit, deriva...Read More

## Variance of a Proportion

We know that the variance of a proportion can be either direct variance or the inverse variance. We use the variance proportion to find the variance in the different areas. Sometimes we come across the problems where the value of one item increases then simultaneously the value of another variable also increases with it. Let us make it more clearly with the help...Read More