math question

hi, i have a math question that i need help with:

when data are non-numerical but can be ordered, such as letter grades, the mean cannot be calculated directly; but both the median and mode can be found. Last year in Ms. Flag's history course, the final grades were 8A's, 6B's, 3C's, 3D's, and 1 F.

Can you find the mean grade for the grades? If yes, devise a system that finds a mean grade. If not, explain why.

Not sure...I tried assigning points to each letter grade but got confused. I need help. Thank you so much.


kelsey, this type of data is referred to as cateforical data, as opposed to ordinal data such as heights and weights.
To do calculations with categorical data, we need to assign numbers to the categories.
We can do this several different ways, so some experimenting may be necessary.
For your data we could assign 4 to A, 3 to B, 2 to C, 1 to D and 0 to F.
Then we have
8A's, 6B's, 3C's, 3D's, and 1 F =
8*4 + 6*3 + 3*2 + 3*1 + 1*0 = 59 total grade score sum
The total number of grades is
8A's, 6B's, 3C's, 3D's, and 1 F = 21 total rades issued.
The average grade issued with this system is the total grade score sum divided total rades issued. This is
59/21 = 2.81 approx. would be the mean for this data with the assignments given.
As I said, there is no one single system that can be employed to assign numbers to categories, so it must be known what values are assigned to make sense of statistics with categorical data. To answer the question, yes, we can devise a system to find the mean, but it will not be unique.

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