Kindly see the embolded sentence below. I don't know why this author exemplified this slogan so complicatedly (my 10 year old didn't understand it), rather than more basically by using $\|$numbers$|$ as small as possible. Can anyone exemplify this using only single-digit (if you can't, or two-digit) integers please?
A recent working paper by economists Michael Spence and Sandile Hlatshwayo painted a striking picture of job growth in the United States. It’s traditional and pleasant to think of America as an industrial colossus, whose factories run furiously night and day producing the goods the world demands. Contemporary reality is rather different. Between 1990 and 2008, the U.S. economy gained a net 27.3 million jobs. Of those, 26.7 million, or 98%, came from the “nontradable sector”: the part of the economy including things like government, health care, retail, and food service, which can’t be outsourced and which don’t produce goods to be shipped overseas.
That number tells a powerful story about recent American industrial history, and it was widely repeated, from The Economist to Bill Clinton’s latest book. But you have to be careful about what it means. Ninety-eight percent is really, really close to 100%. So does the study say that growth is as concentrated in the nontradable part of the economy as it could possibly be? That’s what it sounds like—but that’s not quite right. Jobs in the tradable sector grew by a mere 620,000 between 1990 and 2008, that’s true. But it could have been worse—they could have declined! That’s what happened between 2000 and 2008; the tradable sector lost about 3 million jobs, while the nontradable sector added 7 million. So the nontradable sector accounted for 7 million jobs out of the total gain of 4 million, or 175%!
The slogan to live by here is:
Don’t talk about percentages of numbers when the numbers might be negative.
Ellenberg, How Not to Be Wrong (2014), pages 77-78. Ellenberg wrote an article on Slate with content similar to these pages.
The point that the author Jordan Ellenberg was trying to make with his example is that you can mislead other people when you quote quantities that can be positive or negative (in this case, a net quantity). Here is an example that shows how you can mislead people while still technically quoting accurate figures. The table shows the numbers of different utensils in the kitchen drawer on Monday and Tuesday. \begin{array}{c|c|c|c|} & \text{Spoons} & \text{Forks} & \text{Knives} \\ \hline \text{Monday}& 4& 1& 0\\ \hline \text{Tuesday}& 2 &3 & 5\\ \hline \end{array} From Monday to Tuesday, the net utensils added to the drawer were $5$, and the knives account for $5$ of the utensils added, or $100\%$. Does this mean that all the utensils that were added were knives? Of course not, because we can see that $2$ forks were also added. The reason this is possible is because we lost some spoons, so the net amount added is smaller than the total number of utensils added ($2\ \text{forks} + 5\ \text{knives} = 7$).
We don't even need to use percentages to mislead people when the numbers are this small. We could simply say, the net number of utensils added to the drawer from Monday to Tuesday is $5$, the same as the number of knives added (technically a true statement), therefore, the knives account for all the utensils added to the drawer. This is an unsound conclusion because by missing spoons, we had room to add some forks, too.
This wouldn't work if we said instead the number of utensils added to the drawer between Monday and Tuesday was $7$, and of those, $5$ were knives, and $2$ were forks. Because the number of utensils added (as opposed to the net number of utensils added) is necessarily nonnegative, there is no room to mislead when we quote percentages/fractions. Knives account for $5/7$ of the utensils added, and forks $2/7$.