This blog’s main intention is, by using storytelling, one can teach the basic concepts of statistics. Most people can recall the stories they read or heard during their younger years. The reason why they remember is that those stories leave an indelible impression on their minds. Let us now begin the story. It is a usual bus stop where two people namely a student and a professor wait for their college bus and engage in a lively conversation, of course dominated by the professor, who thinks, speaks, breaths statistics. For every situation or scene he encounters, he has the ability to explain in statistical terms.

This day the bus is late. The professor tells the student that normally our bus comes at a mean time of 7.36 AM with a standard deviation of 2 minutes. To-day it is already 7.50 AM. I am sure this is an outlier. The bus then arrives. After the bus travels for a while, the student sees an accident involving a motorbike and the conversation resumes.

Student: Professor, these motor cyclists are generally stupid and take unnecessary risks.

Professor: Actually, this risk can easily be quantified. There is this probability distribution called the Poisson distribution. To fit the distribution the population must be very large like the number of vehicle on the ECR at any given time and the probability of an accident taking place is very small.

Student: What do I learn from this?

Professor: Good question. Using Poisson distribution one can calculate the expected number of accidents in any given interval of time and the most likely time it could happen. For example, studies shows that the number of motor vehicle accident is the highest during 2 AM and 3 AM, early in the morning.

Student: Thank you sir. Sounds logical.

Now the bus reaches the ECR toll booth. There is a heavy traffic jam.

Student: It looks like we will take a little while, before we clear the toll.

Professor: To tell you the truth, we can calculate the expected time in waiting using the queuing theory. But for me, since the number of vehicles arriving at the toll are independent of each other and of course very large I would utilize the normal distribution to calculate the expected number of arrivals during a specific interval of time say between 8 and 9 AM and then calculate the average number of arrivals and the standard deviation.

Student: Why would you do that?

Professor: Once I know the average arrival per hour, I can find out the total revenue generated during the period of time and then set up a confidence interval of how much money the toll is likely to generate every hour.

Student: Amazing application sir! Thank You.

The bus is now proceeding towards Mahabalipuram. Now lots of open air shops appear on the scene. Small vendors are selling mangoes from the nearby farm.

Student: Professor, do you know these mangoes are great to eat? You should buy some.

Professor: Good idea. You see these mangoes are riped by several different methods. Broadly speaking one that ripes through the natural process and that takes time and the other through smoke created by burning coal. On the outside both mangoes will look the same. But you should be careful what you buy.

Student: How do you find out, Professor?

Professor: Fairly simple. Look at the color, texture, smell, taste and fibre. It is somewhat similar to tasting wine and classifying them as Bordeaux, Chardonnay etc. Anyway a simple factor analysis will help us to determine the factors by which classification should be done. Then, by using the discriminant analysis we will be able to distinguish them.

Student: Professor, I haven’t studied these topics in my statistics course.

Professor: No worries at all. Sit with me in the bus. I will give you a small lecture. You can then read up the rest. By the way we can do break even analysis for these vendors if we can capture all the relevant data.

Student: Thanks sir. I bet you can select the best mangoes from these ones than I can.

Professor: Of course there is always a probability that I will make a mistake but only comfort is my probability of successful selection will be definitely higher than yours. You see in a sequence of independent selection of mangoes the probability I can select ‘r’ good mangoes and ‘n-r’ bad mangoes can be easily calculated using the Binominal distribution. Then we can compute the expected value and the standard deviation.

Now the bus reaches the campus and parks near the new herbal garden.

Professor: You see, I told Prof. Bala that we should have done a Randomized Block Design when planting these seedlings. This way we could easily separate the block and treatment effect along with the interaction of course. But he was busy with some other commitment.

Student: You see Professor, it really amazes me how lucidly you are able to put across so many theories and concepts. An hour in the bus, I got nearly half a course material. Thank you sir!