I read this after the first year at University of Peradeniya. Although we had learnt statistics and probability in A/Ls and even for some courses during the first year, it wasn’t that intuitive as it’s presented in this book. This book is not an advanced book on statistics, it’s nowhere near a basic textbook. It is a book that tries to make statistical concepts intuitive to the reader. It does not go deep into any mathematical concepts but focuses on the intuitive understanding of statistical concepts.
The Flaw of Relying on “The Average”
I’m writing this about 4 years after reading the book. It’s now really trivial but what I took out from this book is that we should not rely on the “average” alone to make decisions. We should always consider the context and the distribution of the data. Averages can be misleading. Here average can refer to any of mean, median and mode. “Average income of a Sri Lankan” refers to the mean, “Income of an average Sri Lankan” refers to the median, and “Income of most Sri Lankans” refers to the mode. Here’s an example of how a mean value can be misleading.
The Bill Gates Bar Paradox:
Bill Gates walks into a bar and the mean net worth of the people in the bar suddenly increases. It doesn’t mean that the average person in the bar is now a billionaire. The average person in the bar is still the same as before.
Calculating the median here would make sense as it’s less prone to outliers. However, there’s a common misconception about using the median as a better ‘average’ than the mean.
Spinning the narrative with scalar averages
You can sell a different story for the same underlying data by picking either mean or median as your average. Let’s consider the following scenarios.
Scenario 1: Mean decreases, Median increases
Consider the following incomes in a group of 10 people calculated in 2015 and 2025:
Incomes in 2015: $10k, $15k, $20k, $25k, $30k, $35k, $40k, $45k, $50k, $1M
- Mean: $127k
- Median: $32.5k
Incomes in 2025: $20k, $25k, $30k, $35k, $40k, $50k, $55k, $60k, $65k, $300k
- Mean: $67.5k (Decreased)
- Median: $45k (Increased)
A poilitician from an oppossing party who wants to highlight that poverty has increased would point to the mean income. Meanwhile, someone from the governing party would point to the median income to highlight that the economy is booming. In reality, if you get rid of the two outliers (1M and 300k), you’ll see that the incomes have increased in the 10 year period.
Scenario 2: Mean increases, Median decreases
Incomes in 2015: $30k, $35k, $40k, $45k, $50k, $55k, $60k, $65k, $70k, $100k
- Mean: $55k
- Median: $52.5k
Incomes in 2025: $10k, $15k, $20k, $25k, $30k, $35k, $40k, $45k, $50k, $1.5M
- Mean: $177k (Increased dramatically)
- Median: $32.5k (Decreased)
Here, a governing party politician would point to the mean surging from $55k to $177k to highlight the growth in the economy. Meanwhile, the opposition party politician would point to the median income dropping from $52.5k to $32.5k to highlight that the middle class is suffering.
Similar scenarios apply to other scalar measures like the mode, but this just goes to say that you always have to consider the context and the distribution of the data. This specially applies when we present our findings in research, there are even academic papers that either present mean or median without publishing either the standard deviation or the distribution of the data.
Real-World Applications: Cricket Analysis
This book led me into analyzing cricket statistics, which I have always been passionate about. For our machine learning and data mining course at Peradeniya, my group gathered ball-by-ball data of over 1,100 T20I matches and started doing some analysis. We uncovered counter-intuitive patterns about match dynamics and player roles. This work led to our research paper, Uncovering Hidden Temporal Patterns in T20I Cricket Through Ball-by-Ball Data Analysis, published at IEEE ICATC 2025.