Question

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?

Short answer

The sample mean is 23.0, which is not meaningful as the observations belong to categorical data.

Step-by-step solution

Given information

The activities were identified by the following codes.

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

Formula for mean

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

Compute the sample mean 

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.

Identify what is wrong with the result

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.