Friday, January 31, 2020

False Negatives and Cancer.

In the voiceover, Cologuard claims it finds 92% of colon cancers. The ad also provides a generously large and easy legible banner stating that false positives and false negative results can occur. 

The next banner gives more detail.

If your grandparent gets a "Yes" response, what is the probability that they do have colon cancer? If they get a "No", what are the chances they don't have it?

If you've never paid much attention to advertisements before, this is pretty amazing. Usually the fine print is illegible even on a 62" ultra hi-definition tv paused at just the right moment.

So ... thank you Cologuard for being honest and up-front.

Thursday, December 19, 2019

522: Where to start with factoring

You are asked to find the roots and factors of the following polynomial function:
f(x) = x4 – 2x3 – 18x2 + 6x + 45

By the rational root theorem, possible rational roots are
± 1, 3, 5, 9, 15, or 45.

In order to minimize your effort, you know that you should begin with the possibility that is most likely to be a root. Which one is most likely?

Tuesday, December 17, 2019

521: When is an outlier still an outlier?

In a set of data, can the outlier also be the mode or does it stop being an outlier?

520: Dan or Mike? Who's Better at Doodle Jump?

Every year I give this graphic comparing the Doodle Jump stats for @ddmeyer and his friend Mike.

Give a couple of reasons why we could consider Dan the better player.
Give a couple of reasons why we could consider Mike the better player.

Measures of Central Tendency.

Tuesday, April 16, 2019

519: Concavity

I have a question that will help me understand the fundamental definition of concavity. If we have y=x^4, can we say that is concave up from (-inf, +inf) or do we need to say (-inf,0)U(0,+inf)?

Wednesday, December 21, 2016

518: Interpret your results.

Say you had data that told you that
The proportion of all US public school students whose families are low-income:
In 1989, less than ⅓
In 2013, more than ½

Interpret this in a positive way.
Interpret this in a negative way.

Saturday, December 17, 2016

517: What is the function?

Algebra 2:
Write a function for this graph ...

What are some possible values for a,b,c,d?
If I told you it also went through (0,54), what might the leading coefficient be?

I would not use the phrase "in factored form", if I were using this in a review or summative assessment since students should be selecting the form that's most appropriate.  I might use it if we are in the middle of learning about functions for the first time and we hadn't really made the case for the utility of various forms of the equation.