Describing data Block 1 Student Activity Sheet 1. · 2018-04-09 · measures of central tendency: • Mode = $800 per dog • Median = $760 per dog • Mean = $632 per dog a. What

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Describing data Block 1 Student Activity Sheet

Copyright 2016 Agile Mind, Inc. ® Content copyright 2016 Charles A. Dana Center, The University of Texas at Austin

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Give the definitions for the following terms. 1. Measure of central tendency

2. Median

3. Mode

4. Mean





5. REINFORCE Use these questions to review key ideas you learned earlier in this course. Note: You can review earlier topics online, if needed.

a. How can you tell whether or not a question is a statistical question?

b. Give two examples of statistical questions.

c. Give two examples of questions that are not statistical questions.

d. Give an example of a question that will generate numerical data.

e. Give an example of question that will generate categorical data.




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1. Consider the adoption costs of the Chihuahuas in the fundraiser.

a. Record an estimate for the combined cost of the 5 Chihuahuas.

b. What is the adoption costs per dog?

2. Maria can now describe the adoption cost data for the Chihuahuas using three different measures of central tendency: • Mode = $800 per dog • Median = $760 per dog • Mean = $632 per dog

a. What is the statistical question that Maria is trying to answer?

b. Which measure of central tendency best represents the typical cost of a Chihuahua in the fundraiser?




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3. Maria is also interested in adopting a Yorkshire terriers mix. Maria collected data on the adoption cost of 10 Yorkshire terriers: $700, $650, $750, $800, $650, $800, $800, $650, $100, and $100.

Write an expression to find the mean of the costs.

4. The prices Maria used to calculate the mean adoption cost of a Yorkshire terrier were

$700, $650, $750, $800, $650, $800, $800, $650, $100, and $100. Find the other measures of central tendency.

Mean Median Mode




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1. Here are the dog weights that Jacob recorded.

4, 6, 7.5, 15, 22, 23.5, 27, 50, 50, 52.5, 62, 78

a. What statistical question is Jacob trying to answer?

b. What attribute is he measuring?

c. What unit of measure is he using?

d. What is the mode of his data?

e. What is the mean of his data? Explain or show your process.

f. What is the median? Explain your process.




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g. Consider which measure of central tendency best represents the typical dog weight. What are the advantages and disadvantages of each measure of central tendency in this situation? Complete the table.

Measure of

central tendency Advantage Disadvantage

Mode

Mean

Median




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2. REINFORCE Alicia has collected some data about high temperatures for different cities on Earth in May.

a. What statistical question is Alicia trying to answer?

b. What attribute is she measuring?

c. What unit of measure is she using?

d. What is the mode?

e. What is the mean? Show your steps and round your answer to the nearest tenth.

f. What is the median?

g. Which measure of central tendency (mean, median, or mode) do you think best represents the typical high temperature in this group of cities? Explain your reasoning.

High Temperatures (degrees Fahrenheit)




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3. REINFORCE Mary records 11 different dog weights in pounds:

4, 40, 5, 64.5, 15, 70, 22.5, 13, 48.2, 4, 5

a. What is the mode weight?

b. What is the median weight?

c. What is the mean weight of the dogs?




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This is a representation of 10 costs (in dollars) Maria collected for Yorkshire terriers. Notice that in Maria's list of Yorkshire terrier adoption cost, the median is larger than the mean and is closer to most of the data.

1. What do you think made the mean less than the median?

2. Can you think of a different situation where the mean would be greater than the median?




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3. For each strength listed, record the measure of central tendency described.

Mean Median Mode




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1. What differences do you notice in the shapes of the three graphs? 2. Write a definition for each of the following terms.

a. Peak

b. Outlier

c. Gap

d. Symmetry

e. Cluster




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3. Describe the spread of the Yorkshire terrier adoption costs.

4. Often data are described by their center. Which measure of center would you use to describe these data, the mean or the median?

5. Describe the shape of the Labrador retriever adoption cost data. Use the terms cluster, symmetry, peak, and center.




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6. What is the range for each of these data sets?

7. Based on the clusters in the data, what can you say about typical adoption costs for the

three dog breeds?




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Here are 10 grades Marcus earned in math class. His last grade (the 11th) is REINFORCEmissing.

8. Suppose Marcus' mode grade is 90. Which of the 10 grades above could not have been

repeated as the 11th grade?

9. Suppose Marcus' median grade is 75. Could 80 have been the 11th grade? 10. Suppose Marcus' median grade is 75. Could 50 have been the 11th grade?

11. Marcus needed at least a mean grade of 75 to keep from being grounded.

a. Assume Marcus was grounded. What is one possibility for his last grade?

b. Assume Marcus was not grounded. What is one possibility for his last grade?




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1. Take a closer look at the graph for the adoption costs of golden retrievers at the fundraising event.

a. Create a box and whisker plot.

b. Label the parts of the boxplot you created in part a, including key values and key features such as quartiles and whiskers.

2. Create a boxplot representing the adoption cost of the Labrador retrievers.




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3. Find the interquartile range for Yorkshire terrier adoption costs and Labrador retriever adoption costs.

4. Compare the interquartile range and range for the two sets. What can this tell you about

the amount of variability in the sets?




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1. Find the mean absolute deviation for the Labrador retriever adoption costs.

2. Do you see any outliers in Maria's data? If so, list them and justify your answer.




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3. Compare the descriptions of the shape of the graph to the placement of the mean, median and modes. How are they related?

4. How do the modes relate to the peaks and the quartiles? 5. How are the outliers represented in the box and whisker plot?




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6. Students in Cassie’s class participated in a community service project over REINFORCEthe weekend. She surveyed some of them about how many hours they spent on the project.

Community

service hours 5 8 2

3.5 3.25

4 6 2

Find the following measures of center and variability. Round your answers to the nearest tenth.

Center Variability

a. Mean b. Range

c. Median d. Mean absolute deviation

e. Mode f. Interquartile range




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The 6th grade classes at Cluster Middle School are conducting a survey of their classmates. They are studying the length (how many letters) of last names of their classmates. To compare the results for the various classes, they are going to compare the means. But they also want to look at how close the data points are to the mean. They need a measure of variability. The mean absolute deviation will tell them where the values are in relation to the mean.

• A small mean absolute deviation says that the numbers are close to the mean. • A large mean absolute deviation says that the numbers are farther from the mean.

Use this information to compare the dot plots and answer the questions.

Number of Letters in Last Name

This is Colby’s graph, based on asking 6 people. 1. What is the mean absolute deviation of the data is?

1 2 3 4 5 6 7 8 9

Mean = 6




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2. Is Colby’s graph representative of the whole 6th grade?

Number of Letters in Last Name

Here are the graphs for all the students in Mrs. Jones’ class and Mr. Rodriguez’ class. 3. Which class appears to have the most variability in length of last name?

Mrs. Jones’ Class

1 2 3 4 5 6 7 8 9

Mean = 5.6

Mean = 5.8 Mr. Rodriguez’ Class 1 2 3 4 5 6 7 8 9

1 2 3 4 5 6 7 8 9




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4. One class has a mean absolute deviation of 1.8 and the other class has a mean absolute deviation of 0.8. Based on the shape of the data, assign the mean absolute deviations.

This graph represents the length of last names in Mrs. Giles’ class.

5. Oops! They forgot to add the name length of an absent student. When she gets back to

school, Ava Papadopoulos-Hernandez should be added to the graph! What will be the new mean? How will the mean absolute deviation change? (You do not have to calculate the mean absolute deviation, but describe how it will change.)

6. Describe the shape, center, and spread of the data for Ms. Jones’ class by REINFORCE

identifying any clusters, gaps, peaks, symmetry, and outliers.

Mr. Giles’ Class

1 2 3 4 5 6 7 8 9

Mean = 5




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7. Determine the interquartile range for Ms. Jones’ class REINFORCE

8. Describe the shape, center, and spread of the data for Mr. Rodriquez’ class by REINFORCE

identifying any clusters, gaps, peaks, symmetry, and outliers. 9. Determine the interquartile range for Mr. Rodriquez’ class. REINFORCE

10. Describe the shape, center, and spread of the data for Ms. Giles class REINFORCE(including the absent student) by identifying any clusters, gaps, peaks, symmetry, and outliers.

11. Determine the interquartile range for Mr. Giles class. REINFORCE

12. Which class has the greatest variability in their data and why? REINFORCE





Stella's dad is concerned about buying a dog that is too big for their small apartment. Stella measured the height (in centimeters) of 25 dogs and created this stem-and-leaf plot.

1. What are the measures of central tendency for the data that Stella collected?

2. Do you see outliers in her list? If so, list them and justify your answer.





1. You saw how Maria made her decision. Now, try this puzzle to explore how you can make your own decisions about which measure of center to use in different situations. For each situation listed, name the one measure of center that would best represent it.

Mean Median Mode

This best represents… Measure (mean, median, or mode)

the typical answer to a survey, which asks 50 people, "What is your favorite ice cream flavor?"

the typical home price in a neighborhood that has a few very expensive houses and many inexpensive houses.

the typical number of hours students study per week, where answers range from 3 to 10 and are spread evenly across the values.





REINFORCE Classroom activity: Snow Cone Stand Sara is helping her older brother run a snow cone stand over the summer. The first thing they need to do is set their prices. They know it will cost them $0.50 per cone in ingredients and labor. They want to know the typical price of a cone, so they are not charging a lot more or less than the competition. 2. Sara finds 25 stands in the city and records the price of a regular cone. Here is her list:

$0.75 $0.95 $1.00 $0.75 $1.25 $0.50 $0.99 $1.00 $1.25 $1.00 $1.25 $0.75 $0.95 $0.85 $1.30 $1.50 $1.00 $1.25 $3.50 $0.85 $0.95 $0.99 $1.00 $1.20 $0.85

Make a histogram of the values.





3. What is the mean, median, and mode price for a snow cone? 4. Do you see any outliers?

5. What is the range?

6. Which price would you report as the most representative? Why?

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Describing data Block 1 Student Activity Sheet 1. · 2018-04-09 · measures of central tendency: • Mode = $800 per dog • Median = $760 per dog • Mean = $632 per dog a. What