# Marge Orrine is on a slippery slope

August 10, 2005

Quality Update Ponderous Puzzler August 22

Another measure of central location is that of the median, defined as the middle number in a data set when data points are arranged from low to high. For example, the first three data points in Marge's data set are 7, 10, and 13. The mean would be 10:

In this example, the median would also be 10, since this is the middle value in the data set. lowest value middle value highest value 7 10 13 median = 10 This method works well with an odd number of data points, of course. But if the fourth number were 15, one would see that there is no single number in the middle: 7 10 13 15 To compute the median in this case, one would average the two numbers in the center and average them. The average of 10 and 13 is 11.5, representing the median. The mode (which Marge Orrine's boss did not request), is the value in the data set that occurs most frequently. In this example of three data points, there is no mode. If, however, the set of data included these numbers, 7, 10, 13, 13, 15 mode = 13 the mode would be 13, since that number recurs and no other data point does.

## ANSWER:

No. Marge Orrine's birth name is, after all, Marge N. Averra, so it might be predictable that she will find herself in error, as she is in her bold assertion about mean and median. For a set of data, what is known as central location can be described by the mean, median, or mode. The mean is, of course, the most common measure. Marge's formula for this calculation was indeed correct. The diagram below, with a normal distribution, reflects the concept of central location:Another measure of central location is that of the median, defined as the middle number in a data set when data points are arranged from low to high. For example, the first three data points in Marge's data set are 7, 10, and 13. The mean would be 10:

In this example, the median would also be 10, since this is the middle value in the data set. lowest value middle value highest value 7 10 13 median = 10 This method works well with an odd number of data points, of course. But if the fourth number were 15, one would see that there is no single number in the middle: 7 10 13 15 To compute the median in this case, one would average the two numbers in the center and average them. The average of 10 and 13 is 11.5, representing the median. The mode (which Marge Orrine's boss did not request), is the value in the data set that occurs most frequently. In this example of three data points, there is no mode. If, however, the set of data included these numbers, 7, 10, 13, 13, 15 mode = 13 the mode would be 13, since that number recurs and no other data point does.