Question

In Exercises 29–32, Identify the level of measurement of the data as nominal, ordinal, interval, or ratio. Also, explain what is wrong with the given calculation.

Super Bowl The first Super Bowl attended by the author was Super Bowl XLVIII. On the first play of the game, the Seattle defense scored on a safety. The defensive players wore jerseys numbered 31, 28, 41, 56, 25, 54, 69, 50, 91, 72, 29, and the average (mean) of those numbers is 49.6.

Short answer

The jersey numbers are measured under the nominal level of measurement. The mean value equal to 49.6 has no meaning.

Step-by-step solution

Given information

Jersey numbers of 11 defensive players are given, and the average value of the numbers is equal to 49.6.

Identification of the appropriate scale

The mathematical treatment of data depends upon its level of measurement.

Nominal level: Categorical data that does not follow any order but possess specific names/labels are measured under the nominal scale. For example, hair color can be assigned values such as 1 for blonde, 2 for black, and 3 for brunette.

As jersey numbers are mere discrete numbers used to label a player, they can be measured under nominal data.

Identification of the error in the given calculation

Statistical measures like mean and median are not computed in the case of nominal data because they have no meaning as values are not quantitative.

As jersey numbers are not numerical but qualitative data, the average value equal to 49.6 has no meaning.