STATISTICS

A guide to computing and interpreting Coefficient of Variation and Quantile Coefficient of Dispersion

We’ve all heard the saying, “Variety is the spice of life,” and in data, that variety or diversity often takes the shape of dispersion.

Data dispersion makes data fascinating by highlighting patterns and insights we wouldn’t have found otherwise. Typically, we use the next as measures of dispersion: variance, standard deviation, range, and interquartile range (IQR). Nevertheless, we may have to look at dataset dispersion beyond these typical measures in some cases.

That is where the Coefficient of Variation (CV) and Quartile Coefficient of Dispersion (QCD) provide insights when comparing datasets.

On this tutorial, we’ll explore the 2 concepts of CV and QCD and answer the next questions for every of them:

• What are they, and the way are they defined?
• How can they be computed?
• interpret the outcomes?

All of the above questions can be answered thoroughly and thru two examples.

Whether we’re measuring people’s heights or housing prices, we seldom find all data points to be the identical. We won’t expect everyone to be the identical. Some individuals are tall, average, or short. The information generally varies. With a view to study this data variability or dispersion, we often quantify it using measures like range, variance, standard deviation, etc. The measures of dispersion quantify how opened up our data points are.

Nevertheless, what if we wish to judge the variability across datasets? For instance, what if we wish to match the sales prices of a jewellery shop and a bookstore? Standard deviation won’t work here, because the scales of the 2 datasets are likely very different.

The CV and QCD are useful indicators of dispersion on this context.