# 10 Days of Science with Math: Qualitative vs. Quantitative Data Analysis

Today I want to share the difference between qualitative and quantitative data and how that leads to math in your science!

Qualitative observations relate to or involve the quality or kind of something. In the popcorn experiment I mentioned yesterday, the taste of the popcorn, the relative size of the kernel before it was popped, and what the popped corn looked like in the end are all qualitative observations. We recorded what each person thought of the taste of the corn with a scale we’d made up (for example, “good, ok, bad”), but that is largely a subjective observation based on each person’s taste. Likewise, we recorded what the kernel size before popping was using a “small, medium, large” scale. Again, it’s an inexact measurement, but it helps to make these observations. We also looked at the relative size of the popped piece of corn. Was the popped corn “small, medium, or large”? We recorded our results in a data chart and it made us ask another question. Does the size of the kernel affect the size of the popped corn? We wanted to know if small kernels yielded small popped corn and vice versa. We made our predictions and then talked about how we could find out.

This is where quantitative analysis comes in. Quantitative Data is measurable and can be calculated for analysis. In our popcorn experiment, we needed to find a way to accurately measure the size of the popped corn without making relative observations. We decided we could measure the volume of the popped corn by filling a pitcher with the popped corn and using the cylinder shape we could calculate the volume of a cylinder. Remember, we’d used the same amount of kernels by weight for each variety. So, the only thing affecting the volume of the popped corn was the variety of corn- not how much corn we used (an important element of our fair test). Calculating the volume of a cylinder…that sounds like math…in our science!

Now if you don’t know the formula for the volume of a cylinder, you are not alone. Neither do I have that on my brain all the time, but I know it can be found. The volume of a cylinder equals Pi times the radius squared times the height.

We had the kids measure the diameter of the pitcher and calculate the radius from there. Then once the popped corn was in the pitcher, they measured the height of the popped corn in the cylinder and that gave us h. They didn’t do this all alone. We engaged in the activity with them and helped them along with the calculations. This was a few years ago when our oldest was the only one who could do the math once we had all the parts of the formula, but it was a great introduction to how to use math formulas and manipulate numbers.

The resulting calculated volumes of each type of popcorn enabled us to answer our question. Does the size of the seed kernel affect the final volume of the popped corn? But how could we answer this question knowing the volume of each one? Time for more math…this time a graph! Now we had an opportunity to discuss which graph would be the best for helping us to see a relationship. Pie graphs are no good here…how about a line graph? Well, line graphs are best when you have a quantitative value on both axes- numbers to put on each side. In this case, we had one qualitative observation and our calculated volumes. This was a job for the bar graph! On the X axis we could have the names of the popcorn varieties and on the Y axis we’d have a scale to use with our Volume values.

What follows is an interpretation of the graph. We had the observed sizes of the corn and put them on the x axis in relative order from smallest to largest. When the bars were put on the graph, it was easy to see whether or not there was a trend in the data. We were able to clearly see that yes! There was a relationship. It turns out it was a direct relationship and it was in a positive direction. The bigger the seed kernel, the larger the popped volume of the corn. The smaller the seed kernel, the lower the volume of popped corn. That was a satisfying moment indeed.

If you’d like to see pictures and more story of how we did The Great Popcorn Popoff Extravaganza go here. You’ll see that we used some basic household items to do the job- like a kitchen scale and some bowls and a pitcher. A post of the results and graphs are here.

In summary, the more you can quantify the results of an experiement, the more credible your conclusions are because you have the numbers to back it up. Numbers and observations make the math in your science! Now that you have some idea of how to get started and what kind of data produces the math, it’s time to get some more ideas. Starting tomorrow and for the rest of the blog hop, I’ll be sharing specific activities you can do in your homeschool to practice using math in science.

If you have any questions, please ask. I’d be happy to entertain discussion in the comments. Thanks for visiting!

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Be sure to visit these brilliant women during our 10 days adventure between November 7th-18th! I love these ladies and we know you will too.

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