Monday, August 28, 2017

Common Core Algebra II: Students' Heights

Patrick Honner does a wonderful Regents recap over on his blog. In today's post, he discusses this statistics question from the June 2017 NYS Algebra II Regents exam. I started this as a comment on his post, but it of course got a little too out of hand for a comment.

So here is my response. These are the many things I dislike about question 15 and how I would make it better.

1. They list the "data" unordered. Why? Choice (2) would be enticing for a student who doesn't realize this and erroneously thinks the median is a good measure of spread. If the student does realize this, the student might waste their time to order them (and here for no reason at all). Either way, it's not a nice practice.

2. Using a set of data and then asking questions about its summary statistics will no doubt create a scenario where a student could potentially make a data entry error. I realize that the median given in (2) is really wrong and is not a measure of spread, but that's not a nice way to test this skill. The kinder, gentler way to ask a question regarding things like this, without diminishing rigor, is to provide the data and summary statistics. I prefer my students to use their test time thinking, not doing data entry. Recent AP Statistics exams have used this approach as well.

3. In (1), they describe data as having an "even spread." I have no idea what that means. (Even means divisible by two, right? Just checking.) Perhaps they meant consistent. No one will ever know.

4. They use the word spread in the question then use the word spread in one of the distractors. More trickery.

5. To say "data is skewed" is amateurish. The shape of the distribution of these data may or may not be skewed, but the data itself is not. Even looking past the "data is...", it's these kind of subtleties that confirm to me that the the people responsible for this test don't know statistics.

6. As Patrick mentions in his post, the only choice that describes anything related to spread, the standard deviation, is (4). But, alas, it still doesn't answer the question being asked. "Which statement best describes the spread of these data?" None of them. Because even (4) is not a statement that describes the spread, it just mentions a phrase that might be used to describe the spread.

7. If the distribution of the data really is skewed, especially in a small sample, then the standard deviation is not the best measure of the spread, the interquartile range is. This is clearly stated in the Common Core standards.

8. This last one is a petty complaint, and it's more a complaint regarding the disorganization of these exams. In the state supplied scoring key and rating guide, the Common Core standard "cluster" is misidentified for this question [see left]. They label this as a question about functions, which it clearly is not. We should be providing correct standard indicators so that teachers can better help their students, especially if this was a question on which the students didn't perform well.


So here's how I would make the question better.

Student's Heights 1.0 (one-question multiple choice version)
Student's Heights 2.0 (five-question multiple choice version to be used, perhaps, as a formative assessment)

Read more:
Patrick Honner, Regents Recap — June, 2017: More Trouble With Statistics
June 2017 NYS Algebra II Regents exam
June 2017 NYS Algebra II Regents scoring key and rating guide


  1. This would be completely inappropriate for middle/high-school students, but there are actually a number of useful robust measures for spread. Probably the easiest is the Median Absolute Deviation, MAD = median(abs(x - median(x))), which has the same efficiency as IQR but works even better against outliers. Then there's some work by Rosseauw and Croux (Sn and Qn), and then more recently by Garth Tarr (Pn).

    Thought you might find those interesting!

    1. Yes, all of those things would be completely inappropriate for middle and high-school students. MAD is not in the Common Core standards (although is sometimes mentioned in a statistics or physics class). Neither is any of the work from anyone you have cited. If you are curious about what is appropriate, I direct you to the GAISE Report linked on my Stats Things Loved page:

      I think you'll find it interesting!!

  2. Thanks for the comprehensive follow up. And I like how you offer improvements! Let's hope someone is reading.