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+--- Thread: [MATH] Median vs. Average (/showthread.php?tid=137484)
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[MATH] Median vs. Average - Drew - 06-14-2012
Student grades need to hit a certain median. Previously, we needed to hit a certain average, but now they want us to hit a median. I can calculate the median value on the spreadsheet. However, I'm having a difficult time figuring out how to "massage" the grades to hit the median. When I had to hit a certain average, it was easy to just multiply each grade by some value (95%, 105%, etc.) to adjust each to make the average. But, that doesn't work with determining the median.
For example, let's say I have 20 students with grades ranging from 60 to 90. The school wants me to hit a median of 78. How can I easily make adjustments to the grades up or down to hit the target median value?
Hope that makes sense.
Edited to change "mean" to "median".
Re: [MATH] Median vs. Average - davester - 06-14-2012
I think it's basically the same. Find the multiplier that makes the current median equal the desired median then multiply all the grades by that multiplier. I'm pretty sure that'll work, though I don't know what you'll do with grades that then end up being over 100% or less than zero.
Re: [MATH] Median vs. Average - Buzz - 06-14-2012
find the median as originally scored, then multiply/divide, as needed, by x to hit your target (78), then multiply/divide the rest of the values by x to redistribute?
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Re: [MATH] Median vs. Average - freeradical - 06-14-2012
Changing how you report your data from mean to median implies something, and I don't think I like it.
You should choose how you report your data depending upon what your data is.
For example, home prices are typically reported in median values because there tend to be lots of outliers in real estate data. By using median values, you get a better feel for what prices are really like.
What would be the most honest way to represent your data?
Re: [MATH] Median vs. Average - Chakravartin - 06-14-2012
freeradical wrote:
Changing how you report your data from mean to median implies something, and I don't think I like it.
How is it substantively different from grading on a standard curve which determines the distribution of the grades before an exam is even taken?
Re: [MATH] Median vs. Average - Drew - 06-14-2012
freeradical wrote:
Changing how you report your data from mean to median implies something, and I don't think I like it.
You should choose how you report your data depending upon what your data is.
For example, home prices are typically reported in median values because there tend to be lots of outliers in real estate data. By using median values, you get a better feel for what prices are really like.
What would be the most honest way to represent your data?
Not my choice, school changed the rule.
Buzz's suggestion looks good. I'm going to try that.
Re: [MATH] Median vs. Average - Buzz - 06-14-2012
I'm a database guy, and the problem looked to be to normalize the data around a median of 78...
Re: [MATH] Median vs. Average - space-time - 06-14-2012
For example, let's say I have 20 students with grades ranging from 60 to 90. The school wants me to hit a median of 78. How can I easily make adjustments to the grades up or down to hit the target median value?
as suggested, multiply/divide to hit the median. It's exactly the same thing you did before with average. Why do you say "When I had to hit a certain average, it was easy to just multiply each grade by some value (95%, 105%, etc.) to adjust each to make the average. But, that doesn't work with determining the median."?
it should work.
Alternative: add or subtract a few points to all grades. this will shift the median up or down by how many points you add or subtract
Re: [MATH] Median vs. Average - RgrF - 06-14-2012
Flunk anyone below average, the fallout will come with a detailed explanation.
average/mean/median
Re: [MATH] Median vs. Average - Drew - 06-14-2012
space-time wrote:
For example, let's say I have 20 students with grades ranging from 60 to 90. The school wants me to hit a median of 78. How can I easily make adjustments to the grades up or down to hit the target median value?
as suggested, multiply/divide to hit the median. It's exactly the same thing you did before with average. Why do you say "When I had to hit a certain average, it was easy to just multiply each grade by some value (95%, 105%, etc.) to adjust each to make the average. But, that doesn't work with determining the median."?
it should work.
Alternative: add or subtract a few points to all grades. this will shift the median up or down by how many points you add or subtract
Thanks. When I used to adjust to hit an average, I had one cell that I would enter an adjustment value in (for example "1.1") . Then in the adjusted grade cell I entered the following formula "=SUM(F4*$G$3)" (in this example F4 holds the adjustment value (for example "1.1") and G3 is the cell that contains the original grade value) . So, to adjust to hit the average I would just enter different values into the adjustment value cell and all grades with that formula would automatically adjust.
I think that Buzz's solution which you noted should work.
Thanks to all.
Edited. Ignore the smiles, they're supposed to be parentheses.