In December 2004 the Seattle Post Intelligencer ran an article titled “State slips behind in school spending” subtitled “Administrators release study, call for Legislature to act.” The article notes:
Washington ranked 34th in the nation for per pupil spending during the 2002-03 school year, spending $7579 per pupil compared with the national average of $8428
In an earlier article we noted that Washington is also concerned about their student/teacher ratio, and that upon closer inspection of the data it appears that this concern may be warranted. The original Seattle P-I article cited several statistics to sell the case that more money is needed for Washington state schools. Is the per-student spending as dire as the class size issue?
The actual data for all 50 states for the 2003-2004 school year is shown at right. It too looks vaguely reminiscent of a bell curve, albeit somewhat less reminiscent than the class size chart. One key difference that people who regularly examine these types of curves will note is that the bell is lop-sided. That is, one end is further from the middle than the other end. When this happens the use of the phrase “average” can be misleading. Most of the time the average and “middle value” or median mean the same thing. That is, the average also implies that ½ of the states spend more than average and ½ of the states spend less than average. But when the bell is lop-sided then the outliers can skew the average away from the middle value. This is one reason why the original article mentioned both rank (34th in the nation; a sense of the median) and average spending.
The average and the median for the actual data are shown above, but to illustrate this point let’s swap a pair of values, the 9-10 bar with the 13-14 bar. The hypothetical data that would support this swap would be 2 states spending between $9,000 and $10,000 per student and 9 states spending between $13,000 and $14,000 per student. This hypothetical situation is shown at the right. Because of this change the average spending per student has increased by $600 but the median hasn’t changed at all, both groups of states were already above the median, and swapping them didn’t change that, but more states are now below the average than before.
Back to our real example, the national average spending per student was $8300, but there was a relatively large number of states that spent more than $13,000 per student. This pushes the average higher than it otherwise would be. The intelligent question should be “how much should we spend per student on education?” But neither the newspaper article nor the quoted school administrator pursued this question, instead they merely compared Washington state’s per-student spending to other states’ and the national average. While Washington is below the national average, it is in the median range and perhaps the national average would be closer to the median if it weren’t for this large number of higher spending states. Why did these states spend so much more than the others and, more importantly, did they get their moneys’ worth?
We’ll examine that question in our next and final article.