Intro to Statistics (Unit 1)

Statistics & probability in high school is often saved for 12th grade, though some progress has been made with integrating linear regression into algebra classes.
My school operates on trimesters, so each class is only 12 weeks long. We’ve created an Intro to Statistics class to focus on descriptive statistics during those 12 weeks. It’s really designed for students who are entering high school, not leaving it. I probably should have created this post a couple of months ago, since the term ends on Tuesday, but I’ve been a little busy.

All About the Chips

Early in the term we investigated claims made by Keebler and Chips Ahoy about their chocolate chip cookies. Of course, in order to really investigate, we needed to dissect the cookies and count up the chips. Here are our results (from this term):

• Fifty percent of Keebler cookies have more chips than 100% of Chips Ahoy.
• Keebler has a mean of 34.4. chips per cookie. With 24 cookies per package, this means there are approximately 860 chips per package.
• Chips Ahoy has a mean of 25.9 chips per cookie. With 35 cookies per package, this means there are approximately 907 chips per package.
• Although Keebler has fewer chips per package, they have more than 25% more chips per cookie (on average) than Chips Ahoy. Keebler would need to have an average of 32.4 chips per cookie for their claim to be true. They had an average of 34.4 chips per cookie, which is more than 25% more chips per cookie.

Students were asked to write an introductory paragraph and a concluding paragraph. Here’s one introduction:

Are they lying? That’s the question we asked ourselves when we conducted tests to see if either Chip’s Ahoy or Keebler told the truth in their advertisements. Chip’s Ahoy promised 1000 chocolate chips in every bag, and Keebler promised 25% more. Our findings surprised us.

The findings followed, and then this conclusion:

We believe, based on our findings, that Chip’s Ahoy told the truth, while Keebler tried to get away with a misleading slogan. While Chip’s Ahoy had approximately 907 chips per package, which is 93 less than they promised, it would be unreasonable to expect our estimate to be exact, as some cookies may have more chips than others. Because of this, we must grant Chips Ahoy some leeway, as it could simply be our estimate was low. However, Keebler promised 25% more chips than Chips Ahoy. However, the total number of chips in Keebler was actually less than Chips Ahoy. However, we believe “25% more” may be referring to the number of chips per cookie, not per package. Because of this, Keebler may be technically telling the truth, but they are misleading consumers. Chips Ahoy was telling the truth all along.

All About the Class

We also collected some data about the class, including height, arm span, and kneeling height. Students were asked to apply what they learned from the cookie activity to the this new data set. They represented the data graphically:

And then described what they saw:

The height is skewed to the left, whilst the kneeling height is symmetrical. Kneeling Height has a small interquartile range, and is less spread out than height. The minimum Height is larger than the maximum kneeling height. Kneeling Height and Standing Height do not share a single point.

They are similar because they are both a measure of distance/height. They are different because a person’s kneeling height will never be greater than their standing height, which leaves interesting data with you compare the two.

There is less variation in kneeling height than there is in standing height. No one in the class was so tall their kneeling height was greater than the minimum standing height recorded.

Or:

Height: The data for height are skewed to the left with a median of 170.5 cm and an interquartile range of 10 cm.

Armspan: The data for armspan are skewed to the right with a median of 166.3 cm and an interquartile range of 11 cm.

Comparison: The median of both sets of data have a difference of 4.2 cm and the interquartile range has a difference of 1 cm. The Height data are skewed to the left while the armspan data are Skewed to the right.

Conclusions: In conclusion, the rule of thumb that you are as tall as your arms are long is mostly true because the median of both data sets is only 4.2 cm off and the fact that the interquartile range is but one centimeter off proves this further.

All About What They Learned

The first unit of the course ends with students finding and analyzing their own data. Data choices included movies, bass fishing, hours in space, world series appearances, touchdowns scored by the Giants and the Cowboys, wealth vs age, costliest hurricanes, and daily high temperatures for Portland, ME and Berlin, Germany. What I love the most about this assignment is that students are able to investigate something that interests them and show me what they’ve learned.

They always come up with topics that I would never think of!