As I’m on vacation on Beaver Island, I’ve been reading for pleasure. I came across a confidence interval in Neal Stephenson’s Seveneves.

As a team of astronauts looks down at soon to be destroyed Earth:

“Layepersons understood it as certainly between 717 and 723 days. Scientists would instead say that if you could repeat the experiment of blowing up the moon a large number of times, and keep track of the time-to-White-Sky separately in each case, the numbers would fall into a normal distribution, a bell-shaped curve, with about two-thirds of the instances falling in that range.”

A fun, summer read and the setting isn’t bad here either.

Each year I always have to decide what to do after the AP Stat Exam. Should I dive into ANOVA tests? Watch Moneyball? I never seem to have a clear plan in mind. Twitter found me this year’s project.

Microsoft recently announced its age-predicting algorithm How-Old.net. I submitted my own picture, was a bit shocked, and then moved on.

(For the record I’ll be 30 in September. My dad will 60 next year!)

I would have been happy to feel a little depressed and move on if it weren’t for @giohio’s Twitter post.

So I begrudgingly convinced 7 fellow colleagues to submit a photo and reveal their true age. Could a measly sample size of 8 determine the accuracy of Microsoft’s algorithm?

The table provided is the summary statistics for Actual Age – Predicted Age. With a mean difference of -5.625, one might believe that the algorithm does overestimate the age of individuals. However, a large standard deviation exists that suggests taking a look at the shape of the distribution as well.

The box plot indicates a distribution that is skewed to the left. This is good news for me, as my picture was one of the larger overestimates in age. A skewed distribution may indicate that the median may be the more representative measure of center. With a median difference of 0.5, evidence may now suggest the algorithm does well at predicting the age of individuals.  Even with all the variation in predictions, do we have evidence to claim that that Microsoft’s algorithm is inaccurate?

Consider the scatterplot of predicted age versus real age.

Our least-squares regression equation is: predicted age = 62.08 – .257(real age). This would indicate the older you are, the younger the algorithm believes you to be. Maybe Microsoft is just secretly trying to boost self-esteem of our older generations while putting youth back in line?

While the sample size is very small (n = 8), the residual plot seems to indicate that this model is appropriate.

Consider a 1-Sample T-test for the following hypotheses:

Null: μ = 0 , we believe there to be no difference between the actual and predicted ages.

Alternative: μ ≠ 0, we believe there is a difference between the actual and predicted ages.

(Again, a small sample size leads to missing conditions for the test. But here are the results.)

We are provided with a t-score of -1.0637 and p-value of .3228. This means we fail to reject the null hypothesis, and evidence suggests there is no difference in actual ages and predicted ages of faculty members in the sample.

When my students tackled the problem, I encouraged them to identify their population of interest. Some groups chose the student body, but not all did. One group tackled the characters from Game of Thrones. Did the actor’s age match the actual age for the show and the books. Another student set out to see if the students in the Breakfast Club were actually predicted to be high school age. This project was a fun way to wrap up the year and pose a task that can be answered in multiple ways.

Any suggestions for revisions or questions, please let me know.

Here’s an interesting article about family income’s impact on college enrollment.

You Draw It: How Family Income Affects Children’s College Chances

The interactivity is neat. Applets like this can go a long way to encourage discussion. First, they provide a percentile rank of you compared to other “drawers”. Second, the graph shows a dotted line representing the vertical distance between your line and the actual line (a.k.a. residuals). I really enjoyed the phrase, “Your line was not steep enough: There is more inequality than you think”.

Interesting connections to rate of change, function behavior, and context. What would your students draw?

This is my endeavor into the world of educational blogging. I currently teach high school math in Indianapolis, Indiana. Right now, my courses are Geometry and AP Statistics. I’m particularly interested in problem solving tasks with a low entry point that are “mathematically deep” and encourage technology and collaboration.

I hope this blog serves as a way share my thoughts, communicate with others, and grow professionally.