I know there is no correct answer to this problem, but it seems a very common question among students who receive their own grade and want to be able to understand what it means.
They know (with example data):
- lower bound: 0
- upper bound: 100
- Std Dev: 23.32
- Mean: 87.07 Median: 95
- Their own grade: 98
And they want to visualize the data in some way, in order to understand, did I crush it, fail hard, or pretty much do the same as the rest of the class.
I understand that I can not render a graph fro the data
But I did make some fake data that matches this data.
Student score 1 87.07 2 95 3 95 4 95 5 95 6 95 7 95 8 95 9 0 10 90 11 92 12 80 13 95 14 98 15 98
avg: 87.00466667 Median: 95 Std Dev: 23.67277561
My question is, what constraints does standard deviation put on the data? Can that help me understand how many students may have failing grades for instance?
I think I completely understand that Median is the middle, so to have a very high median like the sample data would mean most students are scoring very high.
I think I understand Mean also, the average of the students is also pretty high.
Is that correct?