Identify the level of measurement of the data and explain what is wrong with the given calculation. In a set of data, movie ratings are represented as 100 for 1 star, 200 for 2 stars, and 300 stars for 3 stars. The average (mean) of the 527 movie ratings is 231.2.

I got ordinal for the level of measurement,but I don't know what is wrong with the given calculation. Is there not enough information present to get a mean?

Correct.

http://drdavespsychologypage.homestead.com/Two___Two_____four.pdf

Mean only valid for interval or ratio data.

You are correct in identifying the level of measurement as ordinal, as the movie ratings can be ordered but do not have a consistent interval between them.

Regarding the given calculation, there seems to be a discrepancy in the data representation. The statement mentions that the movie ratings are represented as 100 for 1 star, 200 for 2 stars, and 300 for 3 stars. However, the average (mean) of the 527 movie ratings is given as 231.2.

This calculation does not align with the provided data representation. It is unclear how the actual movie ratings are transformed into the given numbers (100, 200, 300), and as a result, it is not possible to determine the correct average (mean) of the movie ratings based on the information given.

In this scenario, the level of measurement for the data is indeed ordinal. Ordinal data is a type of data where the values have a specific order or ranking, but the difference between the values is not necessarily meaningful or consistent.

Now, let's discuss what is wrong with the given calculation. The issue lies in the conversion of the movie ratings to numerical values (100, 200, and 300) without considering the magnitude of the differences between the ratings. By assigning values of 100, 200, and 300 to represent 1, 2, and 3 stars respectively, we are implying that the difference between 1 and 2 stars is the same as the difference between 2 and 3 stars. However, this assumption may not hold true.

Since the rating values are not equally spaced, calculating the mean (average) of 231.2 using these converted values does not accurately reflect the intended interpretation of the ratings. The mean, which is a measure of central tendency, is usually appropriate for data that has an interval or ratio level of measurement where the difference between values is consistent and meaningful. In this case, the mean of 231.2 does not provide an accurate representation of the average rating because the assigned values do not have equidistant differences.

To obtain a meaningful measure of central tendency for this data, it would be more appropriate to use the mode (the most frequently occurring rating), or to employ other statistical measures specifically designed for ordinal data.