ER Codes In an analysis of activities that resulted in brain injuries presenting at hospital emergency rooms, the following activities were identified by the codes shown in parentheses: bicycling (12); football (14); playground (22); basketball (27); swimming (40). Find the mean of 12, 14, 22, 27, and 40. What is wrong with this result?

The activities were identified by the following codes.

• bicycling (12)
• football (14)
• playground (22)
• basketball (27)
• swimming (40)

The mean of n sample values, expressed as x, is $\overline{x}=\frac{\sum x}{n}$.

The count of observations is 5(n).

The values of x are 12,14, 22, 27, and 40.

The mean is computed as follows.

$$\begin{gathered} \overline{x}=\frac{\sum x}{n} \\ =\frac{12+14+22+27+40}{5} \\ =\frac{115}{5} \\ =23 \end{gathered}$$

Thus, the mean is 23.0.

The sample mean value of 23.0 makes no sense.

The sample mean determines one of the central measures, which is the arithmetic average of the entire data set.

The data provided here are for the set of codes for different activities.

The mean of codes is not meaningful as they are a kind of categorical data.

Thus, the result has the meaningless value of the sample mean as the data is categorical.