It is important to understand measures of Dispersion in Statistics. This equips the Manager with a more powerful analysis skill as compared to just understanding measures of Central Tendency.

A basic measure used to summarize data is the measure of “Dispersion”

Dispersion measures indicate the spread of data points around the central tendency measure

(say mean), and give an idea of variability in the data.

There are different ways to measure Dispersion as well, and we need to use the

appropriate measure, given a situation.

Some popular measures of Dispersion are:

1)Range

2)Standard Deviation

3)Inter-Quartile Range

4)Coefficient of Variation

*RANGE*

Measure of dispersion

Difference between largest & smallest observations

## Case Study

Mr. X had to cross five different states on his way from Delhi to Bangalore. The petrol prices were different across states. What is the range of petrol prices?

Rs. 45 Rs. 47.50 Rs. 48 Rs. 46.50 Rs. 49.50

Ordering the data from least to the greatest, we get:

Rs. 45 Rs. 46.50 Rs. 47.50 Rs. 48 Rs. 49.50

Highest – Lowest = Rs. 49.50 – Rs. 45 = Rs. 4.50.

The range of petrol prices is Rs. 4.50

## Interquartile Range

Difference between third & first quartiles

e.g. If you have 100 numbers (not 1 to 100 but some 100 numbers), the number that falls between the 25th & 26th position when the numbers are ranked in ascending order is called the 1st quartile(Q1); the one that falls between the 50th & 51st position is the 2nd quartile; and the one that falls between the 75th & 76th position is called the 3rd quartile (Q3). Basically, you order the data and break into four parts containing equal number of observations

Inter-quartile range measures the spread in the middle 50% of the data Interquartile Range = Q3 – Q1

## Caveat: Not affected by extreme values (as values below Q1 and beyond Q3 are not used in calculating IQR). This makes the IQ range a very important measure Of Dispersion in Statistics

### For Case Study on understanding Interquartile Ranges using a BOX Plot refer our *article here on Box Plot*

## Interesting Note: The second quartile is also called the Median (Q2) – This number will be in the middle with 50% of observations above & below

*Variance & Standard Deviation*

- Most commonly used measures
- These measures take into account the distribution of data between the extreme values, unlike the Range
- These measures indicate the spread of the data around the mean (
*x- in case of*sample mean or**m****–**population mean**)**

## Coefficient Of Variation

- Measure of relative dispersion
- Always a %
- Shows variation relative to mean
- Used to compare 2 or more groups

*Skewness*

Skewness gives an idea of how far to the left, or how far to the right is the data distribution skewed, as compared to a symmetrical distribution. Left skew is also called positive skew, and right skew is called a negative skew. Some graphical examples are given below.

*Kurtosis*

Kurtosis is another measure of shape that indicates if the distribution is sharp & peaked or if it is flat, when compared to a normal distribution.

I am commenting to let you understand what a remarkable encounter my wife’s daughter gained checking yuor web blog. She discovered several things, most notably how it is like to possess an awesome giving character to let many others without difficulty know just exactly specified multifaceted issues. You really surpassed our own expectations. I appreciate you for churning out such necessary, safe, educational and as well as unique thoughts on your topic to Evelyn.

I was pretty pleased to discover this page. I need to to thank you for ones time due

to this wonderful read!! I definitely liked every little bit of

it and I have you saved as a favorite to see new information in your blog.

https://personaliloans.com/

[url=https://valtrex1.com/]order valtrex onlines[/url]

[url=https://carinsurancequotes.us.org/]car insurance in texas[/url]

instant cash online

best personal loan