## Putting a value on college education

Recently I read a piece in Time.com about high school dropout rates. According to this article, the economic outlook for high school dropouts is bleak. The statistics cited by the article are the average earnings and unemployment rates. In 2009, an average college degree holder earned $1,015 per week and an averaged high school dropout earned just$454 per week. The unemployment rate for the college degree holders is 5.2% and 14.6% for high school dropouts. The figures speak volume. They not only put a dollar value on college education. These numbers also give me an opportunity to talk about the concept of ratio, which is a handy way to compare two quantities.

The numbers I want to focus on are the two weekly earnings of $1,015 and$454. How much larger is $1,015 over$454? In terms of absolute amount, the weekly earning of $1,015 is$561 more than $454 since $1015-454=561$. But the absolute amount does not tell the whole story. We can also look at the ratio of$1,015 over $454, which is obtained by$1,015 divided by $454. $\displaystyle (1) \ \ \ \ \ \ \ \ \ \ \frac{1015}{454}=2.236$ What to make of the ratio 2.236? First, it says that the average earning of a college graduate is 2.236 times of the average earning of a high school dropout. For each one dollar in income for a high school dropout, the average college graduate makes two dollars and twenty four cents. So on average a college degree holder makes over two times more than someone with less than a high school education. In this ratio, the baseline (or denominator) is the average weekly earning of a high school dropout. We can also state the ratio 2.236 in terms of percent. Multiplying it by 100, we get 223.6. So the average earning of a college graduate is 223.6% of the average earning of a high school dropout. This is the same information as in the above paragraph, just that the scale is a little different. For each one hundred dollars in income for a high school dropout, the average college graduate makes two hundred and twenty three dollars and sixty cents. The average college grad’s weekly paycheck is$561 more than the weekly paycheck of an average high school dropout. The additional amount of $561 as a percentage of the paycheck for the average high school dropout is: $\displaystyle (2) \ \ \ \ \ \ \ \ \ \ \frac{561}{454}=1.236$ Note that the answer in (2) is just one less than the ratio in (1). Thus the ratio (1) above has another interpretation. Subtracting one from the ratio (1) gives the percent increase going from$454 to $1,015. The increase is 1.236 (or 123.6% after multiplying by 100). For example, if someone is currently making$454 a week and if his income is to increase to $1,015 a week, this represents a 123.6% raise! This is the average premium of a college education, i.e, the additional amount a college grad can expect to make. We can also flip the ratio in (1) and obtain the following ratio. $\displaystyle (3) \ \ \ \ \ \ \ \ \ \ \frac{454}{1015}=0.4473$ What to make of this ratio? Now the baseline is the college graduate. It tells us that the average earning of a high school dropout is only 0.4473 (or 44.73%) of the average earning of a college grad. For each one dollar earned by a college grad, the high school dropout only makes about 44.73 cents. For each one hundred dollars earned by a college grad, the high school dropout makes about fourty four dollars and seventy three cents. If we subtract one from the ratio in (3), we get the percentage change going from$1,015 to $454 (percentage decrease in this case). Note that $0.4473-1=-0.5527$. Multiplying this by 100, we get negative 55.27%. This says that going from$1,015 to $454 represents a 55.27% decrease in income. So if someone is currently making$1,015 a week, and if his income is to decrease to \$454 a week, this represents a 55.27% decrease in income.

To summarize, when we compare two quantities $P$ and $Q$ with $Q$ as a baseline, we can calculate the ratio $\displaystyle R=\frac{P}{Q}$. The ratio $R$ gives information about the quantity $P$ as a percentage of the baseline quantity $Q$.

The quantity $R-1$ is the percentage change going from the baseline quantity $Q$ to the quantity $P$. If $R-1$ is a positive number, then it is a percentage increase when going from $Q$ to $P$. Otherwise it is a percentage decrease. In our income example in this post, $R-1$ can be interpreted as the additional earning of college graduates expressed as a percentage.