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.
To find the mean grade for categorical data, such as letter grades, we need to assign numerical values to each category. In this case, we can assign 4 to A, 3 to B, 2 to C, 1 to D, and 0 to F.
To calculate the mean grade, we need to find the total grade score sum and the total number of grades issued.
For your data, the total grade score sum would be:
8A's * 4 + 6B's * 3 + 3C's * 2 + 3D's * 1 + 1F * 0 = 59
The total number of grades issued would be:
8A's + 6B's + 3C's + 3D's + 1F = 21
To find the mean grade, we divide the total grade score sum by the total number of grades issued:
59 / 21 = 2.81 (approx.)
So, with the given assignments, the mean grade for this data would be approximately 2.81.
It's important to note that there is no one single system that can be applied to categorial data to assign numerical values. The values assigned should make sense in the context of the data and the analysis being performed. Therefore, it's crucial to know the specific values assigned in order to make sense of statistics with categorical data.