Absolute Dispersion Standard Deviation

This topic mainly deals with Economics, which helps to give you an idea of different types of data. If there is a large amount of data, then arranging such a huge amount of data becomes a tedious task. This could take hours of your efforts. This is where absolute dispersion and standard deviation come into play.

You will learn these topics easily in-depth with the help of this article. Learning Statistics in Economics is fun. All you need is a positive mindset and a good start. With this, you are ready to get into deep with your topic. Let’s learn about the absolute dispersion formula and standard deviation formula from scratch. 

What do you mean by Dispersion?

Dispersion, as the name suggests, means to spread. Depression in Economics means the extent up to which data can vary from its average value. In easy words, dispersion helps to convert complex data into simpler ones. The study of the distribution of data in Statistics is known as dispersion. 

Different Benchmarks of Dispersion

It helps to distinguish the extent of data, which means the extent of homogeneity or heterogeneity of data. To interpret the data in simple words, it’s necessary to measure the absolute dispersion. You get to know if the data provided to you is either squeezed or dispersed. 

Types of Dispersion Measures

Broadly, there are two types of measure of dispersion in Economics which are listed as follows.

Absolute Measure of Dispersion

In this type of dispersion, whenever you calculate the result, the result of that unit is always the same as the actual data set provided to you. 

Relative Measure of Dispersion

Whenever we compare between two or more sets of data provided, it is known as the relative measure of dispersion. The measurement of data takes place without the units. 

Absolute Measure of Dispersion

The Absolute Measure of Dispersion describes the variation of data with respect to the average value of different deviations like standard deviation and mean deviation. There are mainly four types of absolute measures of dispersion.

Pillars of Dispersion

Range

If there are different data sets, then you need to subtract the minimum and the maximum value. For example, if the data set is 5,3,9,2,6 then the range would be.

Range= Maximum value – Minimum value

Maximum value= 6

Minimum value= 2

Range= 6-2= 4

Hence, the range would be 4. 

Variance

This means the extent or measure of the distribution of data. The mathematical expression of variance explains you need to subtract the mean from your given data, square each data individually, add all the squares and then divide the obtained result from the number of values that have been provided in your data set. Variance is defined by the Greek symbol sigma. 

Variance(s2) = (xi-x)2(n-1)

Where, S2 is simple variance

xi  is the value of one observation

x is the mean of all the observations

n is the number of observations

Standard Deviation

The measure of deviation from the mean value in the data set is known as the standard deviation. Mathematically, whenever you square root the variance, you obtain the standard deviation. In the standard deviation formula, Standard Deviation is also defined as S.D.

= V2

Where, is known as standard deviation 

Quartiles and Quartile Deviation

Whenever the values are divided into quarters by numbers, it is termed as quartiles. The distance between the first and the third quartile divided by two is known as the quartile deviation.

Mean and Mean Deviation

Whenever you take out an average of different numbers, it’s mean. After observing a given set of data, when you take out the arithmetic mean of the absolute deviation, it is known as mean deviation. 

What is Standard Deviation?

The extent of deviation from the mean value of a given set of data is known as standard deviation. In one word, it means the deviation of value from its average. If there’s a small change in one of the values, the whole standard deviation gets disturbed. That’s why it is dependent on all types of values provided in the data set. It doesn’t depend upon the origin of the data set but depends upon the scale. The Standard Deviation helps to solve the difficult problems of Economics easily. 

The Steps to Calculate Standard Deviation

In order to calculate standard deviation, you must be clear with its formula. The steps for calculating standard deviation are given below. Use these steps to solve any problems based on standard deviation easily. 

• Step 1: Whenever you are provided with a set of data, the first and foremost thing which you need to do is to calculate the mean of the given data. The mean is calculated by summing all the given data and dividing it by the number of observations. 

• Step 2: After you have calculated the mean, you need to subtract this mean from every observation and also note down the square of each value aside. 

• Step 3: At this step, you need to calculate the mean of the newly calculated squared deviations. Again, this would be achieved by adding all the squared data and dividing them by the number of data. This would yield the mean of the square data set. 

• Step 4: The mean that you obtained at the last step is also known as a variance. But to calculate the standard deviation, you need to do the square root of that value. This would help to derive the standard deviation.