## Estimating the Mean & Standard Deviation from a Frequency Distribution?

This week I covered a unit of descriptive statistics – mean, median, mode, quartiles, range, standard deviation, variance, … One section that I struggled with was the one on estimating the mean & standard deviation of a set of data based on a frequency distribution.

As far as estimating the mean goes, I can understand covering this. We want a value that we can consider “typical”. But might it just be better to discuss the median as the estimated measure of central tendency? In other words, isn’t knowing that the median is towards the beginning of the 40-49 class almost as useful as knowing that the estimated mean is 42.3?

The calculation for the estimated mean is not difficult, so covering it will not overwhelm the students. The same is not true for estimating the standard deviation. That is one tedious process, and distracts students from the big picture. I stopped covering that in class long ago, and have not felt one bit of remorse.

Here’s my question – if there were an online tool that made it easy to calculate these two measures (input number of classes, midpoint & frequency for each class), would there be any justification to continue to teach these two topics by hand? I like how the TI-84 handles these calculations, but I do not use the calculator in my classes. If there was a web site that did these calculations just like the TI-84, I would have my students quickly calculate the mean and standard deviation and interpret their results.

So, can you make the case that I should continue to teach my students to make these estimates by hand? I’d love to hear your thoughts.

– George

I am a math instructor at College of the Sequoias in Visalia, CA. If there’s a particular topic you’d like me to address, or if you have a question or a comment, please let me know. You can reach me through the contact page on my website – http://georgewoodbury.com.