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LAKE WOBEGON FOLKS are all above average, yet how many of them know the difference between median and mean? This time, I’m not referring to that strip of land between freeway directions of travel, nor a lack of generosity.
This occurred to me reading a recent study published by the Pew Research Center comparing traditional book reading with its electronic equivalents, such as reading e-books and stuff on computer screens or smart phones.
”Book Reading 2016” is fascinating (and, ironically, likely perused online).
A summary of the research appears in ”No, the Internet Has Not Killed the Printed Book. Most People Still Prefer Them, by Daniel Victor in The New York Times, September 2, 2016, also online.
The distinction of median versus mean comes up in the Pew study’s Appendix A: Additional demographic tables and charts. These offer data on the number of books read per year by the average American. What’s more, the data are identified by gender, ethnicity, age, education, income and residence (urban, suburban or rural).
I won’t spill the variegated beans (reading the report is too much fun for that). However, let’s take one aspect as an example of median versus mean. Pew queried a representative sample of U.S. adults, ages 18+, about the number of books read, in whole or in part, per year. The median was 4 books per year; the mean, 12.
Median and mean, which is which?
The mean of a set of values is its arithmetic average. In other words, add up the values and then divide by their number. For example, consider the data array 1, 2, 2, 3, 5 and 8. Its mean is (1+2+2+3+5+8)/6 = 21/6 = 3.5
The median is that data point in the middle when they’re arranged in order. (Think middle of the Interstate.) If, as in our little array, there’s an even number of data, and hence no “middle” one, the median is midway between the middle pair, i.e., their mean. Our median: (2+3)/2 = 5/2 = 2.5.
By way of completeness, there are other measures of data: mode and range. Mode is the value that appears most often, if there is one; in our example, 2. Range is the difference between largest and smallest value; in our example, 8–1= 7.
In a distribution of data that’s relatively uniform, the median and mean will be close to each other. If data are skewed one way or the other, median and mean values can be considerably different.
Note the medians, our 2.5 and Pew’s 4, are smaller than their respective means, our 3.5 and Pew’s 12. I don’t have access to Pew’s raw data, but I suspect that, like our data array, its distribution is skewed.
Said another way, I’d guess many folks read relatively few books, but those who do read more books read a lot more of them. ds
© Dennis Simanaitis, SimanaitisSays.com, 2016