In The Data Set, Course Grades Are Represented As 1

In the set of data, course grades are represented as 1 for 'A', 2 for 'B', and 'C'

In the set of data, course grades are represented as 1 for 'A', 2 for 'B', and 3 for 'C'. The average (mean) of 751 course grades is 1.3. The data are what level of measurement? what is wrong with the given calculations? A.one must use different method to take the average of such data. B. Such data should not be used for calculations such as an average. C. The true average is 2.5. D. there is something wrong with the given calculations.

Paper For Above instruction

The data under consideration involve categorical grades represented numerically as 1 for 'A', 2 for 'B', and 3 for 'C'. When such data are analyzed, the key question pertains to their level of measurement, which influences the appropriateness of statistical operations like calculating the mean. The levels of measurement, as established by Stevens (1946), include nominal, ordinal, interval, and ratio. Nominal data represent categories without intrinsic order, ordinal data indicate rank order, interval data have meaningful distances between points, and ratio data possess a meaningful zero point.

In this context, the coding of grades as 1, 2, and 3 reflects an ordinal nature because letter grades imply a rank order: A is superior to B, which is superior to C. However, these codes do not necessarily possess equal intervals, nor do they represent true numerical quantities with consistent differences. As such, the level of measurement for this data is primarily ordinal.

Calculating the mean of ordinal data is often problematic because the mean assumes equal intervals between data points, an assumption that does not hold for categorical grades. In this case, the average grade is 1.3, which is a numerical summary that may imply a grade slightly better than 'A', yet such an interpretation is misleading because the underlying data are ordinal and not interval. The choice of averaging ordinal ranks presumes equal differences between ranks, which is usually unwarranted.

The problem with the given calculations lies in the misuse of the mean as a measure of central tendency for ordinal data. Using the mean can distort the true nature of the data, and such an average does not accurately reflect the distribution of grades because the difference between 'A' and 'B' may not be equivalent to that between 'B' and 'C'. Additionally, the average of 1.3 seems to suggest a grade better than 'A', which is impossible given the data coding.

Therefore, the correct perspective is that these data should be treated as ordinal, and statistical analyses should utilize appropriate measures such as the median or mode, which do not assume equal intervals. The median, in particular, would be a more suitable measure of central tendency for this data set, as it indicates the middle value in the ordered set, respecting the ordinal nature of the grades.

Regarding the options provided, option B, which states that such data should not be used for calculations like an average, is the most accurate. While averages can sometimes be calculated for ordinal data to provide a rough central tendency, they are often misleading or inappropriate without considering the data's measurement level. Some statisticians argue against calculating means for ordinal data entirely, favoring medians or modes, because these do not require interval assumptions.

In summary, the main issues are the level of measurement—these grades are ordinal—and the misuse of the mean to summarize data that do not meet the assumptions necessary for averaging. To properly analyze these grades, using median or mode would provide more valid insights, and the reported average of 1.3 should be interpreted with caution.

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