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 for 3 stars. the average (mean) of the 527 movie ratings is 231.2
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To identify the level of measurement of the data and explain what is wrong with the given calculation, we need to understand the four levels of measurement: nominal, ordinal, interval, and ratio.
In this case, the data is represented in a numerical format, but the numbers assigned to movie ratings (100, 200, 300) do not have inherent numerical meaning. Therefore, we can conclude that the level of measurement is nominal. Nominal data are categorical, where numbers are used as labels or codes to represent categories.
Now, let's discuss what is wrong with the given calculation. Since the assigned numerical values for movie ratings do not have a standard numerical interval, we cannot assume that the difference between 100 and 200 is the same as the difference between 200 and 300. This means that we cannot treat them as interval data.
The average (mean) calculation assumes that the data is measured on an interval or ratio scale, where the differences between values are meaningful and consistent. However, in this case, the average (mean) of 231.2 does not accurately represent the movie ratings since the numerical values assigned to each rating are arbitrary and lack a true numerical interpretation.
To obtain a meaningful average (mean), it would be necessary to use a different approach. One option would be to recode the ratings on an interval or ratio scale, where equal intervals between ratings exist. For example, you could assign values such as 1, 2, 3 for 1, 2, 3 stars, respectively. This would allow for a valid calculation of the mean movie rating.