Social Issues · Student Life

The Power of Charts

Hey, everyone! This would be one of the math-intensive posts that I will be sharing so bear with me!Capture

(Taken from https://www.instagram.com/berniesanders/)

This graph showing the disparity in after-tax income savings due to a new policy change in the US. The difference between the household earnings of <$10k and >$1 million is quite significant, differing by a factor of ~2115 times! However, as I would explain, this bar chart has some issues. For one, the x-axis is in a range and is unevenly distributed. Furthermore, it disregards the fact that tax savings are a function of income. Hence, a more appropriate chart would be as shown below.

Capture 1

Adjustments I have made:

1. I have adjusted for the range by taking a simple average of the 2 extremes. Since there is an unlimited upside for household income >$1 million, I have estimated the average to be at $2 million.

2. I have divided the tax savings by estimated income for each segment to get an estimated percentage.

Hence, the difference of factor 2115 has been reduced to a factor of 4. As can be seen here, there is still a significant difference between the high and low-income groups in terms of household income savings. However, this can be attributed to the large number of tax deductions the poor would receive vis-a-vis the rich. The lower base of taxable income for the poor will push up the tax savings as a percentage of taxable income for the poor while for the rich, the taxable income would be about the same as household income and so, the percentage would remain flat.

In conclusion, how charts are presented can sometimes lead people to think one way instead of the other and so, we must consider carefully the axis of the chart, what the trend says about the 2 variables, as well as any sharp points of inflexions that may mean something. This would enable us to view charts more accurately and avoid being misled.

Advertisements
Social Issues

A story on Racism

This was inspired by a video that I saw on Facebook.

It was a typical Monday afternoon, and an Indian construction worker was waiting to meet his doctor. He fidgeted nervously in his seat. He reeked of sweat and grime, having toiled the earlier half of the day to build a new housing estate just beside the doctor’s office. His doctor had asked him to come down for no particular reason today, so he was quite curious as to what was happening.

The doorbell chimed and a family of three entered the doctor’s office. They were a typical family, consisting of a Caucasian father, a Caucasian mother and a Caucasian girl, who was no more than 5 years old. The girl immediately plopped on the seat next to the Indian worker and shot him a beaming smile. He returned the smile, something he had not done for a very long time.

Her parents were not so polite. With a face contorted with disgust, and against the will of her daughter, she pulled her daughter to the next seat and sat down gingerly next to the Indian. After a while, she too felt uncomfortable and her husband replaced her while she stood at the side awkwardly as there were only 3 seats available outside the doctor’s office. Just when the Indian worker’s wanted to stand up from his seat to let the woman sit together with her family, the doctor’s voice boomed from his office.

“Alice and family, you can come in. Abdul, come in too!”

The family and Abdul quickly made their way into the office. The doctor immediately extended a warm greeting to the family.

“Hello, Bill, Sarah, and Alice! I haven’t seen you in a while! How is Alice?”

Bill replied, “She is doing very well! The bone marrow transplant was a life-saver for her! It is all thanks to you, Doctor!”

“No, it is not me that you should thank. It is Abdul. He provided the bone marrow for the transplant,” the doctor exclaimed, with his hand firmly on Abdul’s shoulder.

Bill’s jaw dropped in surprise. Sarah began crying profusely as emotions overwhelmed her. Alice was instantaneously upon Abdul and hugged him. Abdul laughed sheepishly as he gingerly held Alice.

“We are so sorry, so sorry, so sorry…”