Jennifer Waters teaches statistics and personal finance at Trinity Episcopal School, an IB World School, in Richmond, Virginia. She is a long time AP Reader and Table Leader. Jennifer was an Early Table Leader for 2023 Question #1.

As part of a study on the chemistry of Alaskan streams, researchers took water samples from many streams with temperatures colder than 8°C and from many streams with temperatures warmer than 8°C. For each sample, the researchers measured the dissolved oxygen concentration, in milligrams per liter (mg/l).

### Part (a)

The researchers constructed the histogram shown for the dissolved oxygen concentration in streams from all sample with water temperatures colder than 8°C. Based on the histogram, describe the distribution of dissolved oxygen concentration in streams with water temperatures colder than 8°C.

## WOULD THIS GET CREDIT?

Including context is vital to receiving full credit. In addition, students need to indicate at least 3 of the 4 other characteristics of the distribution (shape, center, spread, unusual features) to receive full credit.

### Teaching Tips:

Teach students some kind of mnemonic to remember everything that must be included when describing a distribution: SOCS + context, SOCV + context, or CCUSS are frequently used by teachers.

While peak and mode are interesting features of distributions they are not measures of center.

It is important that definitive language not be used when stating measures of center and outliers. We do not have the actual data to make precise calculations, so everything we suggest is an approximation.

### Part (b)

The researchers computed the summary statistics shown in the table for the dissolved oxygen concentration in streams from the sample with water temperatures warmer than 8°C. Use the summary statistics to construct a box plot for the dissolved oxygen concentration in streams with water temperatures warmer than 8°C. Do not indicate outliers.

## WOULD THIS GET CREDIT?

Full credit was earned if the response provided at least 4 of the 5 features of the boxplot were correct (min, Q1, median, Q3, max).

### Teaching Tips:

Teach students that boxplots (without outliers indicated) span from the minimum to the maximum.

Students should practice constructing boxplots to know that the 5-number summary values are the only measures included in a boxplot. (No mean or standard deviation is included on the plot.)

### Part (c)

The researchers believe that streams with higher dissolved oxygen concentration are generally healthier for wildlife. Which streams are generally healthier for wildlife, those with temperature colderthan 8°C or those with water temperatures warmer than 8°C? Using characteristics of the distribution of dissolved oxygen concentration for temperatures colder than 8°C and characteristics of the distribution of dissolved oxygen concentration for temperatures warmer than 8°C, justify your answer.

## WOULD THIS GET CREDIT?

Answering the question about which streams are healthier for wildlife is vital to receiving full credit. In addition, students need at least 2 of the 3 characteristic comparisons (shape, center, spread) to receive full credit.

### Teaching Tips:

Teach students that comparing two distributions requires words like "greater than" and "less than"; “while” or “only” are not comparative words.

Even when something seems obvious (such as the median values for each distribution), students need to spell it out. Require students to be specific when answering free response.

Thank you for writing this, it is very helpful as I am embarking on my first year of teaching AP Statistics.

I am curious about the answer to part c. The question asks to give reasons why the colder stream is better. I don't see how the ranges being the same or the shape matters in this situation. If the question asked to compare distributions that would be a different story. Any help?

Would students be allowed to use interval notation?

The median is in the interval (11,12)

Thanks so much for writing this - very helpful!

I have a question about the language for the median in part (a). Based on the data in the histogram, we can calculate that the median must be between 11 and 12. Why does the response "the median is 11-12" receive no credit? The teaching step says don't use definitive language, but the median is definitely between 11 and 12.

Really appreciate these insights, especially the emphasis on avoiding ”definitive language” when we don’t have the data to support it! This has been a challenge — getting comfortable with number sense and estimation — for many of my students coming from advanced algebra courses that emphasize exact numbers.