AP Stats Unit 1 Practice FRQ Prompt Answers & Feedback

Unit 1 FRQ Practice Prompt

FRQ Practice Submission 1

In part (a), you make a clear comparison of shape, spread, and center, and your answer is in context. Your descriptions of shape are correct, your comparison for spread is correct, but your comparison for center is incorrect (the median time for both distributions is between 15-16 minutes - check it again!). If this were a stand-alone scoring rubric, you would earn a “partial” for this question (having done 3 of the 4 required things). If it had multiple components, you would earn “essentially correct” (E) for all parts except the part that contained the comparison of center.

In part (b), you correct link the shape of the distribution after 8:00am to the likely impact on the mean commute time, AND explain how that is not true in the distribution before 8:00am. You would earn “E” for this portion. Nicely done!

FRQ Practice Submission 2

In part (a), you make a clear comparison between the spread of the two distributions (“the range is larger when he leaves after 8AM as compared to when he leaves earlier”), but you do not do the same for your description of the median time (“on the other hand” does not count as a quantitative comparison). Additionally, check the graphs again - the median for the “after 8:00am” distribution should also be between 15-16 minutes. Your descriptions of shape are correct and your answer is in context. Having done 3 of the 4 components correct (compare shape, compare spread, in context), you would earn “partial” for this question.

In part (b), you make a correct claim about the mean commute time being larger when he leaves after 8AM vs before 8AM, but your explanation could use a little more clarity. When you say “the histogram,” and then “the second graph”, you should be careful to specific which histogram you are referring to, and explain why the “second graph” doesn’t have the same feature as the first. Your answer might get an “E” if the rubric is generous, but would likely earn “P”.

Nicely done - there are a few minor tweaks that will get you up to full credit in no time, so keep practicing!

FRQ Practice Submission 3

In part (a), you make a clear comparison of center (“same median time”), clear comparison of spread (“is greater than the range of travel time for before 8 am”), a correct description of shapes, and your answer is in context. This checks all the scoring boxes, and would earn “E” for essentially correct.

In part (b), you give a clear explanation of why the right-skew in the “after 8 am” distribution would impact the mean commute time, and tie in your work from part (a) to strengthen your argument. This would also earn “E”. You did a good job of giving a thorough answer without “talking too much” and giving up credit that you had already earned. Well done!

FRQ Practice Submission 4

You’ve done a good job of getting to the point in both parts (a) and (b) and saying exactly what you need to say without much more. Your answer in part (a) includes appropriate comparisons and the context of the problem, and your answer in part (b) mentions the impact of shape on the mean/median in BOTH histograms, which is important for communicating your answer. These should both earn full credit as responses!

FRQ Practice Submission 5

In part (a), you do a good job of describing the distributions of commute times, but you do not compare them. If the AP exam asks you to “compare” distributions, they’re looking for you to use explicit comparison terms, such as “greater than,” “less than,” or “equal to.” Also, be sure to explicitly compare the shape, center, and spread of distributions. You mention the shape and spread of each distribution (without comparing the spreads), but do not give a measure of center for either distribution (mean or median; “peak” is a nice thing to describe but will not count as a measure of center). You could have strengthened your response by adding comparison statements at the end of your paragraph (for example, “the commute times after 8am have a larger range than before 8am”). As it stands now, you would not receive credit for your response.

In part (b), you do a good job of clearly communicating your choice (after 8am) and why it’s your choice (“skewed right”), as well as why the other graph is not your choice (“its graph is not skewed”). Good explanation! This would earn “E” (full credit).

FRQ Practice Submission 6

In part (a), you do a good job of comparing the distributions in context. Your comparison of medians is correct, and your comparison of spread is correct (quick note - you could have used “variability”, “range”, or “standard deviation” to make these comparisons - you did not need to include all three statements Similarly, you only need to compare one of the two measures of center - median or mean). Be careful with your descriptions of shape - you called the before 8:00am graph “normal”. While it would be fair to call it “approximately normal,” to be a true “normal” distribution the graph would have to meet certain criteria that we are not able to check without more information. On some rubrics, that would ding you and prevent you from earning full credit. Really, any time you want to say something is “normal” on the AP exam, you should add “approximately” to it (unless you’re explicitly told something is in fact Normal).

In part (b), you do a good job of clearly explaining your choice of graph, and connecting it to the fact that skew impacts the mean. You would likely earn full credit.

FRQ Practice Submission 7

In part (a), you do a good job of making in-context comparisons, correctly comparing the median and range for the two distributions, and making comments on the lack of obvious outliers. Be careful with your shape comments - typically the description “unimodal” by itself is not enough to earn full credit (as a distribution can be unimodal and symmetric, or unimodal and skewed). “Bimodal” by itself is a good description for shape, but you should include “approximately symmetric” or “skewed to the ___” with any unimodal description.

In part (b), you choose the correct histogram and clearly defend your choice with a reference to the mean being impacted by the skew of the histogram. Nice job!

FRQ Practice Submission 8

In part (a), you make clear comparisons of center, shape, and spread in context of the scenario. One thing to be careful with is your mention of “the center” being the same. As you (correctly) argue in part (b), the median travel times are within the same range, but the mean travel times are not, due to the skewness of the “after 8:00am” graph. Therefore, your use of the generic term “center” may be penalized, as there are two measures of center you may be referring to (median/mean) and only one of them is likely “the same.” It’s important to be specific in cases like that.

As mentioned, your answer to part (b) is very good - it thoroughly explains your choice and why the other choice is incorrect. Well done!

FRQ Practice Submission 9

In part (a), you make a clear comparison of the shapes of the graphs and a clear comparison of the spread/variability. [Sidenote: be careful talking about ranges on histograms. The ranges are approximately 7 and approximately 10 minutes, respectively, because the numbers on the x-axis for a histogram are endpoints of intervals. The longest commute time after 8:00am may not have been exactly 22 minutes; it could have been 21.6 minutes.] Unfortunately, even though you name the mean/median (center) for each distribution, you don’t ever explicitly compare them, as the prompt asks. When asked to compare distributions, you must make an explicit comparison (“less than,” “more than,” “equal to”, “similar to”, etc). Even though you imply the centers are similarly around 15 minutes, you have to spell it out for us.

In part (b), you correctly cite the right-skew having an impact on the mean and choose the correct distribution (and explain why the other one is wrong), but I think you have some typos (you say “mean” every time but I think you meant to say “median” at least once there).

FRQ Practice Submission 10

In reading your descriptions, I think you may have switched labels in part (a) - it looks like the first thing you describe is the “after” graph (range of 10, skewed right, etc)… but you called it the “before” graph. Additionally, while you give good descriptions, you don’t ever compare the centers & spreads explicitly. When asked to do a comparison of graphs, we have to “spell it out” by saying things like “greater than,” “less than,” etc. Also, some things to be careful with in your descriptions: (1) it’s impossible for a distribution to be both “approximately normal” and “strongly skewed right”, (2) when discussing range on a histogram, we must use language like “approximately 10 minutes” - we can’t actually be sure what the max/min values are unless we’re explicitly told. (example: the shortest commute time might be 12.4 minutes). I don’t mean this to sound like your response was all bad - you clearly have some understanding here - but I do want you to know how to attack these kinds of questions.

Moving on to part (b), you give a clear explanation of your choice, with correct reasoning in both cases. Well done!

FRQ Practice Submission 11

Your answer to part (a) is very thorough, and addresses the scenario in context with comparisons of center, shape, spread, and a discussion of outliers. One small thing - be careful in your shape comparisons. It’s good to describe the after 8am times as skewed, but “unimodal” by itself for the before 8am times is a little too general. “Bimodal” as a shape can count as full credit, but “unimodal” typically does not - as you can be unimodal and symmetric or unimodal and skewed (in fact, the after 8am graph is unimodal as well in this case). You should go with something like “more symmetric” to earn the full credit.

In part (b), you give a very clear (correct) answer with reasons relating to the shape of the graph. I have the same note about “unimodal” vs “symmetric”.

FRQ Practice Submission 12

In part (a), you give a very thorough comparison, including shapes, center, and spread. You also say “about 10 minutes” for the range after 8am, which is important on histograms (as you can’t know the min/max values for sure).

In part (b), you pick the wrong distribution. Remember that the mean is impacted by skew/outliers - so the majority of data on the left (AKA skewed right) will actually have a higher mean than median (as the few data points on the right will skew the mean, but not the median). Therefore, it is the after 8am distribution in this case.

FRQ Practice Submission 13

In part (a), you provide appropriate descriptions of center, shape, and spread for each of the distributions, but you do not provide comparisons. Comparisons in AP Stats involve explicit comparison words like “more,” “less,” “about the same as,” etc. For an example of this in action, see the post shortly above yours by user “abar2648”.

In part (b), you give a clear description of how mean is impacted by the skew in the after 8am distribution. Nice job.

FRQ Practice Submission 14

Nice responses! You have clear comparisons in part (a) of center, shape, and spread. You could strengthen part (a) by referring to “median” as your measure of center in this part - the means will likely be different as you correctly defend in part (b).

FRQ Practice Submission 15

Both answers are very solid and written in a way that would earn points on typical rubrics. You provide clear comparisons in part (a) of center, shape, and spread, and provide a strong description in part (b) that is in context and mentions both distributions. Nice job!