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Hello! My stats team had some questions about definitions and methods for computing statistical measures with multiple accepted methods.
Outliers- Informal assessment, compute by hand, compute with technology? All of the above?
Quartiles- There are various methods to identify the quartiles. Do we need a particular approach or must students simply be able to explain the method they choose?
“5-number summary” is a phrase AP stats students must know. For vertical alignment, if we use this phrase can you anticipate any problems aligning with the CCSS?
Skew- Do students need to be able to distinguish between skew left or skew right? I recall from AP stats that this was a counter-intuitive answer. I ask because the standards don’t include the word “skew” but the progression has an example (pg 3) which labels the different graphs.
Technology- In the Geometry forum, I asked you about dynamic geometry software and accessibility issues. Your reply was technology is neither required or forbidden. Is it correct to assume that answer doesn’t apply for this conceptual category? We could use small data sets and have students compute by hand but it appears as if technology is required to fully meet the goals for this category.
Our group has only met once so I’m sure we will have many more questions later. Thanks for your willingness to help us process!
Lots of questions here and I’m not sure I have answers for all of them. I’ll take the easiest one first: it seems to me that some software for dealing with large data sets is a must in the statistics standards. A lot of the statistical measures don’t make much sense for small data sets (why on earth would you want to know the median of the set {1, 2, 2, 3, 5, 9}?). Also, it is only for small data sets that the different definitions of quartile make any serious difference, and getting into those distinctions is most certainly a waste of time. I think for most of the measures you discuss above, students should be looking at large data sets using technology, in which case the software will be reporting the measures. Students should understand what they mean and how they are computed.
Some of your questions seem to be about vocabulary. There’s no harm in introducing vocabulary (skew left, skew right, five-number summary) as long as the vocabulary doesn’t become the topic. For example, I would want students to be able to look at two distributions, one skewed one way and one skewed the other way, and identify the one in which the median is greater than the mean. I don’t much care whether they know which one is skewed left and which one is skewed right, at least not on a test, although obviously it is useful to have consistent terminology that students can use as they talk to each other. The same goes for five-number summaries. Students should be able to identify the minimum, the maximum, the median, and the two quartiles, and they should be able to talk about the differences between two data sets using these measures. The term is good as long as it is understood as useful in those conversations, but not if it becomes a pre-occupation of instruction and assessment.
Hello,
May I suggest a reason why knowing the difference between the terms skewed left (negative) and skewed right (positive) may be not only beneficial, but essential, in understanding the relationship between the shape and context of the data? If students are asked to interpret the differences in shape, center and spread in context (S.ID.3) between the distribution of the age at which people first get a driver’s license and the distribution of the age at which people retire, part of understanding this data in context is to understand that in the first instance, the distribution is likely to be skewed positive and in the second, the distribution is likely to be skewed negative.
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