Grade 6

Mid-Unit Assessment

Select all the statistical questions.

How many cups are in a gallon?

Which measuring spoon (tablespoon, teaspoon, half-teaspoon, or quarter-teaspoon) do home bakers use most frequently?

On average, how much salt do professional pastry chefs use in a pie crust?

Which is larger, 17 ounces or 2 cups?

Did a specific store sell more measuring cups or measuring spoons on a specific day?

Answer:

B, C

The dot plot shows the number of hours 20 sixth-grade students spent studying in a week.

<p>A dot plot. Hours spent studying.</p>

Select all true statements about the data used to build the dot plot.

The difference between the most hours and the least hours spent studying was 6 hours.

The mean amount of study time was 5 hours.

Nine students studied for at least 4 hours.

Every student studied at least 1 hour.

Only 1% of the students studied more than 6 hours.

Answer:

A, C, D

Teaching Notes

Students analyze a dot plot, including simple questions about spread and distribution. Students are asked to calculate percentages: There are 20 data points to make calculations simpler. Students who select Choice B were visually looking at the dot plot giving an approximate value for the mean instead of calculating the mean. Students who don’t select Choice A may not have noticed 0 did not have a tick mark and took that as the lowest value. Students who don’t select Choice C may have misinterpreted the term “at least.” Students who select Choice E have a misunderstanding about 1% versus the data of one student.

A survey asked people how many hours they spend watching television during a week, to the nearest hour. The histogram displays the data.

Which of these statements must be true?

<p>A histogram. Number of people. Hours spent watching television.</p>

Every person in the survey spent less than 10 hours watching television.

Every person in the survey watched some television during the week.

There are more people in the survey who watched 12 hours of television than people who watched 17 hours.

More than 20 people participated in the survey.

Answer:

Teaching Notes

Students who select Choice A may have confused the meaning of the two axes. Students who select Choice B do not understand that a histogram’s bin includes its left edge value, in this case 0. Students who select Choice C are looking at the size of the bin and drawing a conclusion that a histogram is not capable of making.

Here is the height of 20 flowers in the school garden, in centimeters.

Draw a histogram to display the data.
Based on the histogram, what is a typical height for these 20 flowers?

<p>A coordinate plane. Height. Centimeters.</p>

Answer:

Sample response: About 40 centimeters. Most of the flowers are 40–60 centimeters, with very few flowers more than 60 centimeters.

Tier 1 response:

Accurate, correct work.
All histogram bar heights are correct, and the typical length given is in the 30–55 cm range.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: One or two mistakes in histogram bar heights; correct histogram but a typical length above 55 cm given.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Major mistakes in histogram bar heights; attempt to draw a different type of plot; mistakes in histogram and an incorrect typical length; empty or nonsensical answer to typical-length question.

Teaching Notes

For the second question, accept any answer from 30 to 55 centimeters. The mean of the data is 42.25 centimeters, but students should not need this calculation to answer the question. The problem does not specify the intervals students must use, so accept alternate correct histograms. Students are likely to use the intervals provided.

The mean of four numbers is 40. Three of the four numbers are 35, 41, and 41. What is the fourth number?

Answer:

Teaching Notes

There is more than one way to do this problem. Thinking of the mean as a fair share is the intended method. (One number is 5 less than the mean, and two numbers are each 1 more than the mean. Because the four numbers must be evenly distributed around 40, the last number must be 3 more than the mean.) Students may also recognize that if the mean of four numbers is 40, the sum of the four numbers is 160.

Draw two dot plots, each with 7 or fewer data points, so that:
- Both dot plots display data with the same mean.
- The data displayed in Dot plot B has a much larger MAD (mean absolute deviation) than the data displayed in Dot plot A.
How can you tell, visually, that one dot plot displays data with a larger MAD than another?

Answer:

The dot plots should show the same mean, with Dot plot A showing a much tighter clustering than Dot plot B.
Sample response: Since MAD is a measure of spread, the data in a dot plot with a larger MAD will have the wider spread.

Tier 1 response:

Accurate, correct work.
Dot plots show the same mean; Dot plot B has visibly larger MAD; appropriate description of spread given.
Acceptable errors: Dot plots include more than 7 points.

Tier 2 response:

Work shows general conceptual understanding and mastery, with some errors.
Sample errors: Dot plots show a significantly different center but correct MAD; dot plots show correct center but similar MAD; dot plots are correct but backward; no reasonable description given.

Tier 3 response:

Significant errors in work demonstrate lack of conceptual understanding or mastery.
Sample errors: Two or more error types from Tier 2 response; failure to draw two dot plots.

Teaching Notes

Some students may have trouble here constructing the dot plots because the problem is quite open-ended. The guideline of 7 or fewer data points is intended only to limit the amount of time students spend on this problem.

Sodium is measured in food to represent the amount of salt. These dot plots represent the milligrams of salt in 5 popular menu items from 2 different fast food restaurants.

<p>A dot plot. Restaurant 1. Sodium. Milligrams.</p> — Restaurant 1

<p>A dot plot. Restaurant 2. Sodium. Milligrams.</p> — Restaurant 2

For each restaurant, identify any menu item whose sodium is unusual compared to the other items from the restaurant.
Calculate the MAD (mean absolute deviation) of each data set. Which restaurant has menu items with a wider spread of sodium content?

Answer:

Restaurant 1: One unusual value of 1,000. Restaurant 2: No unusual values.
Restaurant 1 has a mean absolute deviation of 160, Restaurant 2 has a mean absolute deviation of 240. Restaurant 2 has the larger spread.

Tier 1 response:

Accurate, correct work.
Correct list of unusual data, correct calculations of MAD, correct selection of Restaurant 2 as having the larger spread.

Tier 2 response:

Work shows good conceptual understanding and mastery, with minor errors.
Sample errors: A calculation error causes one mean or MAD to be incorrect; incorrect list of unusual data; failure to correctly compare MADs with otherwise accurate work.
Acceptable errors: An error in calculations causes an incorrect conclusion about which restaurant has the larger spread.

Tier 3 response:

Work shows a developing but incomplete conceptual understanding, with significant errors.
Sample errors: Two or more error types from Tier 2 response; multiple calculation errors; an incorrect MAD with no work shown; minor errors in chosen method of determining mean or MAD, including failure to use absolute value of deviations.

Tier 4 response:

Work includes major errors or omissions that demonstrate a lack of conceptual understanding and mastery.
Sample errors: Badly incorrect algorithm for calculating mean or MAD; no calculation of MAD.

Teaching Notes

Students analyze the MAD of two data sets. One data set has an unusually high value, while the other is evenly spread. The first set has a lesser MAD because on average it is less spread out.