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Welcome!! Geoboards are riddles for your brain!

Here are some challenges to start:

1. Make a square that stretches the rubber band 20 lengths. (link)
2. Make a shape with 6 sides AND 1 set of parallel sides. (link)
3. Make a triangle that fits two triangles inside of it. (link)
4. Make a shape with 4 sides and no parallel sides. (link)
5. Create 2 shapes that have the same length of the rubber band. (link)
6. Create 3 shapes that have the same area inside of the rubber bands. (link)
7. Create a triangle that has 2 sides the exact same length. (link)

Check back Mondays for more geometry riddles!

Hi, I am a co-author of the STEM Everyday Book written for edMe Learning. I am currently a student at Old Dominion University pursuing a Bachelor’s degree in Business Management and a minor in marketing. I enjoyed playing a role in creating some of the stations we have inside the store and using my artistic skills to make artwork and displays. Because I was hired before the store opened I’ve been able to watch the it grow and see kids and adults come inside to observe the same neat activities and ideas inside the book.

Julia Medina is a co-author of the STEM Everyday Book written for edMe Learning. She is a current student at The University of Virginia pursuing a Bachelor’s degree in Economics.

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Variance describes the distance between each data point and the center. Statisticians realized quickly that if they just added each distance, then the total distance would be 0.

Mean of Scores: 95

Instead of adding 5 + 0 + -5 = 0, statisticians square each distance. This also makes small distances smaller and big distances bigger. So, this variance calculation better describes how far each datapoint is from the mean.

Now the total distance is 25 + 0 + 25 = 50, and the average distance is 50 divided by 3, about 16.67.

Here is an example of finding the variance within a population of two people.

The mean is 25 so the squared distance for both people are 100. The average distance is (100 + 100) ÷ 2 = 100.

This second example has a population of 4 people, and the mean is still 25.

So the population variance decreases to 62.5 because the two new scores are closer to the mean. Your question is based on the idea that the average of 100, 100, 25, 25 is equal to the average of 62.5, 62.5, 62.5, 62.5. We could represent this in the calculation of the total squared distances.

So, if you know the population variance is 25. Then, you could estimate on average that each person has an individual variance of 25. In a sample of 20, the table would look like this:

This means that the Sum of Squared Distances (SS) is 500, on average. If we wanted to calculate a sample deviation, then we would divide SS/df, 500 ÷ 19 = 26.32.

The question is hard conceptually because it isn’t realistic. You almost never know the population variance, and it isn’t used to estimate the variance in theoretical samples.

But, you can calculate SS by estimating that every person in the sample has the population variance. Then, calculating that sum.

If you have any further questions, just shoot me a text! Khan Academy walks through these calculations step by step.