analyzing data

[farmgirlIN]

My son conducted an experiment using differing weights of arrow heads to determine how the weight of the arrow affected the force it could generate. We controlled for distance, the draw, etc. We repeated the experiment until we had 18 square target hits for each of the three grains of arrow head, measuring the depth of penetration. I believe that it would be appropriate to exclude the smallest and largest numbers from our data prior to calculating median and mean to account for possible differences in the density of the target or a difference in the draw. Am I correct, or would this skew the data? It's been a long time since I took any physical science classes.
Thanks,
Heather

[deleted-71603]

Hi Heather. Unless you can explain the "fluke" that caused a data point to be signifcantly different from the other data points (throwing mechanism failed, discovered afterward the arrow was deformed, etc), you never want to exclude data points from your conclusions. Every data point is useful.

There are several reasons / arguments / schools of thought about whether to exclude data or not and how to determine which data points to keep, but that is well beyond elementary level math. Unless you had a catastrophic failure during one of the trials, keep all of your data. It is smart to calculate both mean and median of the data, as long as your son can explain the difference between the two values. If not, I recommend just reporting the average. (median v. mean, I believe, is beyond elementary school math).

Certainly write back if you have more questions or still unsure of what data to use or what numbers to report.

Good luck to your son in the science fair!

[deleted-71709]

Good advice from Deanna. I would recommend keeping all your data also, and for the sake of simplicity, report the mean - that is the average.

However, having said that, it is good to understand how much data varies as well. Sometimes variance, most commonly reported as "standard deviation" in statistical terms, can be very telling about a process. To keep things simple for a second grader, I'd recommend reporting not only the average, but also the difference between the largest and smallest measurement in each case you are studying. Think about what kinds of "normal" factors could account for any changes in these differences from one case to another. For instance, one type of arrow head may flutter more during flight than another, creating more variance in the results.

What ever you do, congratulations for getting involved with your child on this project and HAVE FUN!