## How big is the median household income?

The U.S. Census Bureau announced on September 16, 2010 that real median household income in the United States in 2009 was $49,777. How big is this amount relative to, say, the income from earning the minimum wage? The current Federal minimum hourly wage is$7.25. But states are allowed to set their own minimum wage rates. The hourly minimum wage among the 50 states currently ranges from $5.15 to$8.55. Obviously, the median household income is more than the annual income from full time employment paying the minimum hourly wage. By how much? This post presents a back of the envelop calculation that does not require a calculator or math formula. For the interested reader, the precise calculation is also presented for comparison.

The median household income of $49,777 as reported above is essentially$50,000. Suppose someone is making $1,000 a week. This will add up to$52,000 a year (since there are 52 weeks in a year). Assuming working 5 days a week and 8 hours each day, this means that the person makes about $200 each day ($1,000 divided by 5) and about $25 per hour ($200 divided by 8). So in this back of the envelop calculation, the annual median household income is equivalent to an hourly rate of about $25 per hour. Thus the median household income is about 3 to 5 times the income from full time employment paying the minimum wage. The annual income of$52,000 is more than the median household income by about $2,000. So the estimate of$25 per hour is an overestimate of the hourly rate equivalent to the annual income of $49,777. The precise hourly wage is: $\displaystyle \frac{49777}{52 \times 5 \times 8}=23.93$ Thus the estimate of$25 overestimates by about \$1 per hour. But it still gives the essential information that the median household income is 3 to 5 times more than the minimum wage income (depending on the state). For a rough comparison, this quick and dirty calculation works quite well.