The meaning of statistics

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In response to the Nonprofit DataViz, a letter to the editor from Joe Fioccola

Thanks for showcasing the important work of so many of Asheville’s nonprofits [“Doing Good in WNC,” Nov. 20 Xpress]. A lot of information is gathered in one place, but there is a problem with some numbers in the data visualization by Steph Guinan.

It is misleading when she says, “$3,236 is the median annual contribution for area households compared to the national average of $2,564.” The implication is that each family gave $3,236, but medians and averages are very different numbers. For example, if 10 people give $10 and one gives $1,000, the total received is $1,100. While the median would be $550 and the average $100, the percentage of donors giving either amount is zero. So, unless the national average is actually the average of median contributions, it is like comparing apples and oranges — you don’t get a clear picture of either.

A more useful number might be the percentage of households that give, the percentage of household income contributed and the percentage breakdown between religious organizations and non-church giving, because it would be clear what the numbers actually meant and help guide choices about how much individuals should be giving.

Xpress writer Steph Guinan responds:

Thank you for your thoughtful letter. In the age of big data, an engaged dialogue can help us all to better understand the information that’s available to us. Numbers can be misleading, and we must be careful to use them properly.

You identified an important discrepancy. I should have said “national median of $2,564” rather than national average. The two numbers are actually comparing median to median.

It’s true that in your example, the average is $100. However, the median specifically refers to the middle figure in a sequence of figures arranged from low to high. That makes the median in your example $10, not $550.

As to whether it’s better to use average or median in doing statistical analysis, a comment on this from Chris Roush, senior associate dean at the UNC Chapel Hill School of Journalism and Mass Communication, and Walter E. Hussman Sr., distinguished scholar in business journalism, might be helpful: “While median and average are often very close, the average can be skewed by a few numbers that are not representative of the rest of the data set. In these cases, the median gives a better representation of the numbers.”

Finally, the percent of household income donated was included in the graphic. Asheville Metro gives 6.4 percent of their income compared to U.S. at 4.7 percent.

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