2022 Introduction to Statistics in Research Mitchell 2nd ed

I N T R O T O R E S E A R C H : D A T A V I S U A L I Z A T I O N & C O M M O N S T A T T E S T S

Let's look at the data shown here on crime reported on college campuses. Everything listed here is fictitious. Notice that the crimes range from 0 to 29, and that the student population ranges from 692 to 38,431.

You can tell it has been formatted as a table by the drop-down arrows. It has also been sorted from highest to lowest by the number of crimes. The percent was an added calculation. The mean (arithmetic mean) is the average of the values or the "center" of the data. In this case, the mean can be calculated using Excel using the =Average(b2:b15) or (22,330) for the mean of the number of students and =Average(c2:c15) or (9.6) for the mean of crimes. (Quiz)

The median is the midpoint of a set of data values when you put them in order (either smallest to largest or largest to smallest). It always splits the data into two equal halves. Using Excel, the formula is =median(B2:B15) or 14,211 for # of students and =median(C2:C15) or 5.0 for the crimes. (Quiz)

Table 63: Crime Data at colleges (FAKEData)

You may be asking yourself -"Why is the mean for crimes (9.6) so different from the median (5.0)?

Sometimes it's due to outliers. Outliers are values much larger or much smaller than the rest of the values. Outliers don't have much impact on the median, but outliers can have a drastic effect on the mean. Since the mean is the balance point, extreme values in the data will pull the mean toward it to maintain the balance.

Table 64: Comparing Mean to Median

Here is an eye-opening difference:

In 2020, "the average" (or mean) U.S. household income is $87,864 and the median is $61,937"(Backman, 2020, para 3). This tells the researcher that a few high incomes

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