Interpretation and Use of Dispersion Measures
In our previous blog, we have understood the definition and need of measures of dispersion. It is important to understand the interpretation and usage of dispersion before we get into the mathematical formulae of these measures.
The concept of dispersion is not an easy concept. I am sure most of the blog readers very well know that standard deviation (or variance) is the most used measure to quantify volatility or the spread in data. Many of you will also remember the formula of standard deviation. However very few understand how to interpret or use dispersion.
I will try to explain dispersion in a lucid way. When I come across data having dispersion, I ask myself a few questions:
- How much is the dispersion?
- How do I make use of dispersion in data?
- What are the factors leading to dispersion?
How much is the dispersion in data?
When there is dispersion, the first step is to quantify the dispersion using an appropriate measure like range, interquartile range, standard deviation, or variance. Using mathematical formula you can easily compute the dispersion measures. Having got the value, the next question is what do I do with this measure?
How do I make use of dispersion in data?
Statistic Training example
In our previous blog, we took an example of teaching statistics to engineering students vs data science executive course students. The dispersion is engineering students’ age is less, i.e. they are more homogeneous. Whereas there is more scatter in the age of executive course students, i.e. they are heterogeneous.
How does dispersion in data impact the trainer? How can trainers make use of dispersion in data?
The trainer teaching statistics will be able to easily teach the concepts of statistics to engineering students as the group is more homogeneous. Whereas, the trainer will have to be more prepared while teaching the students of executive program. This is because the executive group is more heterogeneous.
Sales & Marketing example
Assume, you are the marketing head of television making company. The customers purchasing the televisions of your company belong to different age groups, income segments, geography (rural-urban), education level, etc. The very fact that the customers have varied demographic and income profile, leads to the fact that there is dispersion.
The most important question for you as marketing head is – how to use the dispersion in customer profile to increase sales?
The obvious answer to this is:
- Create homogeneous customer segments from the heterogeneous data. By creating homogeneous segments, we are reducing the spread within the segment.
- Design television models with different feature combinations to cater to each segment
From both the above examples we see it is important to understand how to use dispersion.
What are the factors leading to dispersion?
Quite often we know that there is dispersion in data. However, at times we may not be able to directly use dispersion in data for sales or marketing. But it may be important for us to understand the factors that lead to dispersion.
Residential Property Price
Assume you collect data of all the property sales transactions in the city of Thane. The sale of properties may have happened at various prices, probably ranging from Rs. 1 million (Rs. 10 Lakhs) to Rs. 50 million (Rs. 5 crores) and above. There would be instances of significant difference in property prices within a locality, within a tower, etc. All this suggest that there is dispersion in property price.
The question here is – What are the factors that influence the property price?
The factors that influence can be locality, carpet area, amenities, distance from public transport system, schools, malls, and other utilities in the vicinity area, etc.
From the above example, it is evident that understanding the factors causing dispersion is more important in this instance.
Next Blog
In the next blog, we will get into the mathematics and calculations of dispersion measures. We will first start with the simplest measure of dispersion – range
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