A common student error was with interpreting standard deviation.  They tended to use the interpretation from earlier in the year.  For example they would say, “The weight of the Reese’s piece typically varies by 0.002 grams from the mean of 0.8 grams.”  They should reference that this is a mean weight from a group of 30 pieces.  We’ve been using sentence templates for interpretations this year.​

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“The sample mean weight (count, proportion, or mean) from 30 Reese’s pieces (sample size in context) typically varies by 0.002 grams (standard deviation value) from the true mean (mean or proportion) of 0.8 grams (value).”

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In general, we’re not huge fans of just memorizing, but the templates have been helpful.  Many students use them to interpret in their own words, but some students do use the exactly.

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Another common error was with calculating a probability using a normal curve when the problem lacked scaffolding.  If the problem gave the population standard deviation, many students forgot to calculate the standard deviation of the sampling distribution and instead used the population standard deviation.  However, some problems had students calculate the standard deviation of the sampling distribution as part a, for example, and then asked them to calculate a probability in part b.  They had no problems with this.