Measure of dispersion in Statistics

Before we get into the title of this story, let us understand that there are three metrics in statistics that help quantify measurements and summarize a set of information acquired or perceived in order to communicate a large amount of observations in simplest terms.

1. Measure of frequency: Tells us how often something occurs, we can communicate this via Counts, Percentages or Frequency of occurring
2. Measure of central tendency: Tells us the midpoint of set of observations, we can communicate this via Mean, Median or Mode.
3. Measure of dispersion and variation: Tells us how spread out or varied a dataset it, we can communicate this via Range, Interquartile range, Variance, Standard Deviation or Mean Deviation

Let us understand measures of dispersion in detail:

1. Range: This measure is used to get a basic understanding & initial analysis on how spread the values are within a dataset by calulating the difference between max value and min value. It is most useful for small datasets but can be inaccurate if outliers (an element that is noticeably different) are present, as it doesn’t account for values between the extremes.
2. Mean Deviation: This measure is the average distance between each element in the dataset to its mean. Lets say, in a town with 10 people, if the average weight is 48kg, with two people weighing 80kg (32kg away from the average) and eight weighing 40kg (8kg away), mean deviation considers how far each weight is from the average, regardless of whether they are higher or lower.
3. Variance: A measures how much each element deviates from the mean, helping to compare datasets with the same mean. For example, if two companies have the same average stock price of $75, but Company A’s prices range from $60 to $100 and Company B’s range from $74 to $76, variance shows that Company B is more stable, while Company A’s higher variance suggests potentially higher ROI.
4. Standard Deviation: Standard deviation is the square root of variance, which can be hard to interpret since variance gives the square of the measure. Standard deviation, however, is in the same units as the original data, making it easier to understand. For example, if you’re measuring height in feet and inches, the standard deviation will also be in feet and inches.
5. Interquartile Range: Range can be skewed by outliers, giving a false impression of spread. The interquartile range (IQR) addresses this by considering values between the 25th and 75th percentiles, eliminating the influence of outliers. It’s particularly useful for understanding income distribution in a population, as it avoids the skewness caused by extreme values.