Questions: Identify the level of measurement of the data, and explain what is wrong with the given calculation. In a set of data, course grades are represented as 100 for 'A', 200 for 'B', and 300 for 'C'. The average (mean) of the 689 course grades is 231.2. The data are at the level of measurement. What is wrong with the given calculation? A. Such data should not be used for calculations such as an average (mean). B. The true average (mean) is 195.4. C. One must use a different method to compute the average (mean) of such data. D. There is nothing wrong with the given calculation.

Solution Steps

To solve this problem, we need to identify the level of measurement for the data and determine if calculating the mean is appropriate. The grades are represented by arbitrary numbers (100, 200, 300), which suggests an ordinal level of measurement. Ordinal data can be ranked but not meaningfully averaged, so calculating a mean is inappropriate. Therefore, the correct answer is that such data should not be used for calculations like an average.

The course grades are represented as \(100\) for \(A\), \(200\) for \(B\), and \(300\) for \(C\). This representation indicates an ordinal level of measurement, as the grades can be ranked but the numerical values do not have a meaningful interpretation for arithmetic operations.

The average (mean) of the \(689\) course grades is given as \(231.2\). However, since the data is ordinal, calculating a mean is inappropriate. The mean implies that the differences between the values are meaningful, which is not the case here.

Given that the calculation of the mean is not suitable for ordinal data, the correct choice is: A. Such data should not be used for calculations such as an average (mean).

Final Answer