524: Is a HotDog a sandwich?

Does the topology matter? If I were to completely separate the two halves, would it make a difference?

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?

https://www.ispot.tv/ad/op0r/cologuard-finding-things

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.

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?

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.

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)?

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.

Proportion of all US public school students whose families are low-income: In 1989, <1/3. In 2013, >1/2.

— Alfie Kohn (@alfiekohn) December 21, 2016