The final year results were declared and there was a cloud of anxiety, sadness and frustration in the Chang household.
Yue was heartbroken to have missed the Principal’s medal in her school by a mere mark. School passing out results were declared and the top three girls had won the Principal’s medal. The sixteen year old teenager had worked very hard throughout the year, sacrificing her hobbies and sports. She came agonizingly close to bagging the prestigious honor. Along with the honor, the top three students were also automatically selected for the graduation college while everyone else had to undergo a selection process.
Distraught at the turn of events, she flung herself into isolation and barely ate anything for 2 days. Jie – her mother was patient initially but began to worry as the hours ticked by. She called Mei, her younger sibling and Mei visited them soon enough.
Mei was ten years younger to Jie and often joked that she was the sandwich generation in the extended family. Old enough to understand the traditional outlook of her parents and sister and also young enough to feel the pulse of the rebellious Yue and other cousins.
She was a statistician by education, but loved literature. With a penchant for problem solving, she pivoted from academia into consulting and used her skills to build data science solutions.
She knew well enough that Yue must have heard all the usual pep talk from her parents. So, she approached Yue on a very different note.
As she entered Yue’s bedroom, she noticed that the lights were dim. Books and clothes were strewn in a corner. Yue was curled up on the bed staring out at the falling rain. The weather was gloomy and the atmosphere in the room added further to it.
Gently sitting by the bedside, Mei caressed Yue’s head and started speaking. After the usual pleasantries, she dived right into it.
Mei – “I learnt something new last week about numbers. It is called the Anscombe’s Quartet. Let me show you with an example.
She pulled over the whiteboard by the teenager’s table and started scribbling numbers. Yue turned over and looked at the board curiously.
As Yue stretched to see what Mei was doing, she almost got up from her bed and sat cross legged. She noted her aunt had listed numbers in 2 columns.
Mei – “Assume you drove your bike from your home to my place and then we went to the mall, beach and then back home. Consider the time taken in minutes for the 4 subsets of journeys on two different days -
Just by looking at the numbers, you may be tempted to think you spent more time on Day 1.
But calculate the total time taken – it is the same 100 mins and the average time taken is 25 mins.
So, though your mind tricks you into thinking you were slow to start with, on the balance it took the same time at the end of day.
Right?
Yue nodded, wondering what was coming next.
Mei (pulling out her mobile phone) – Now look at these numbers (pairs of x, y coordinates). These are 4 sets of numbers – each set of 11 pairs of x, y co-ordinates.
Look very different, don’t they? But their descriptive statistics are same. Mean of every set is (9,7.5), the variance is (11,4.12) and correlation between x and y in every data set is 0.816
Yue was amazed to see this similarity in what seemed to be a random set of numbers.
Mei went on – “But, the number sets could not be more different, Yue! Look here as she showed the plots of the 4 sets”
Yue (gasped) – “Oh! That’s cool!”
Jie was watching intently what her younger sister was discussing with her daughter. The age gap between the two sisters meant she had almost raised Mei like her own and knew she had a way with words.
Mei looked at Jie and noted the puzzled expression.
(Smiling and with a soft tone), Mei continued – “Like our earlier bike ride, what we see is that on the balance, the 4 sets of numbers are similar. Their trajectories are distinct, but in summary, they end up with the same descriptive statistics. “
“Now imagine these 4 sets of numbers as the milestones in the lives of 4 girls. Maybe the first (x,y) is their school passing marks, the next is their graduation, then their post-graduation, job, first promotion and so on.
If one compares the set at each juncture, one may be fooled thinking one set will end up far better than the other over the long run.
Sure, their trajectories are different – zig zag, slow and steady or quick and bumpy and they look visually distinct. But, on the balance, they are pretty similar.
On the contrary, if you look only at the statistics, you might never know how distinctly different their trajectories are!
There is more than one way to arrive at the summit and each way has its own unique journey!
For some paths, the climb is tough at the start, but eases over time. For some, it is the opposite. Still, for others, it is steady throughout. ”
Mei paused as she saw her niece trying to understand what she was alluding to. She was hoping Yue might pop a few questions. But none came.
So, Mei explained - “Do you remember when you first moved to this school from another country and struggled in the first semester?”
Yue nodded – “I was 10th in class and my grades were all over!”
Mei (pumped her fist) – “But, you put your head down and made up for it in the next 2, what was your rank again by the year end?”
Yue (with pride) – “3rd!”
Mei patted Yue lovingly and continued – “And you had come from a completely different country, schooling style while all the other kids were in the same school…”
Jie jumped in – “… same with the basketball game last year. Your team lost 2 quarters, but how you all made up in the next 2! You were a bunch of nerds filling in for the first team out on injury and still you managed to surprise the regulars from the opponent school. I was so proud of you all! “
Mei hugged Yue and kissing her forehead said – “There is a long journey ahead, little flower! You will get many more chances to bloom and spread your color, don’t wither away like this!”
Now Yue realized what her aunt was saying as tears welled up in her eyes.
Jie hugged the pair as her heart swelled with a mixture of relief and pride. Relief as her distraught daughter was now relaxed and pride as her younger sibling had so swiftly comforted her daughter.
Lovely!!