How Do Mean, Standard Deviation, and IQR Reflect Differences in Data Sets?

[gelfand]

Homework Statement

Compare and contrast the given data

Homework Equations

None needed for this

The Attempt at a Solution

I'm never too sure what kind of thing I'd be expected to do for something like
this.

Here's how I would go about it, but would appreciate any pointers / things to
consider:Representing mock with A, real with B

Mean : A < B implies that the average mark was higher on B

St. Dev : A > B implies that there was a greater spread of marks in A than B

Min, Max : the Min(A) < Min(B) and Max(A) < Max(B), also [Max(A) - Min(A) ]<
[Max(B) - Min(B)] , which implies that the marks were spread out more in A than
B, and supports what was considered from the standard deviation.

IQR: We can find the IQR from the difference between the provided quartiles, so
for A we have ~12 and for B we have ~5.

I'm not too sure what else I would really say about this though?

Thanks

 

[mighty2000]

for sharing your thoughts on this topic! I would approach this task by first looking at the data and making observations about the numerical values. For example, I would note that the mean mark for A is lower than B, indicating that students in B generally performed better on the assignment. I would also look at the standard deviation, which tells us about the spread of the data. In this case, A has a higher standard deviation, indicating that there was more variability in the marks for A compared to B.

I would also consider the minimum and maximum values for each dataset, as well as the range. This would give us a better understanding of how the marks were distributed and if there were any outliers. In this case, A has a larger range, indicating that there were some extreme values that may have affected the overall mean.

Finally, I would look at the IQR (interquartile range) for each dataset. This measure tells us about the spread of the middle 50% of the data. In this case, A has a larger IQR, further supporting the idea that there was more variability in the marks for A compared to B.

Overall, it seems that B has a more consistent set of marks, with a smaller range and IQR, while A has a wider spread of marks. It would be interesting to further investigate the reasons for this difference, such as the difficulty of the assignment or the students' preparation for it.