Vocabulary Station​
: Use the vocabulary list below to use for either option 1 ​
or​
option 2. Have your teacher check after. Statistical Question Typical Frequency Mean Variability Range Dot Plot Deviations from the Mean Mean Absolute Deviation (MAD) Center Data Distribution Balancing Point Option 1: From Here to There 1. Work with a partner or two. 2. Review the list of vocabulary words above. 3. Create a logical path using all the vocabulary words on the list. a. Choose any of the words with which to begin and define it. b. Within that definition use one of the other words on the list. c. Then define that one as it leads to another… d. Each of the words needs to be included in the “chain.” i. Example: The ​
circumference​
of a circle is like the perimeter; it is the distance around the outer edge. To get the circumference you multiply pi and the ​
diameter​
… Option 2: Graphic Organizer­ Choose 3 words above that relate to one another (ie. words for center, variability, general data distributions etc.) to create 3 separate graphic organizers. Lesson 1: Statistical Questions Station​
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Do this station if you missed any of #1 or need extra practice Identify each question as statistical or nonstatistical. If it is not statistical, rewrite the question so it is. 1. How many days of school are left? 2. How many text messages do you typically send in a day? 3. How many hours of TV/computer/phone use do you typically use per day? 4. How many students are in 6th grade at Fallon? 5. How many books have you read this school year? 6. How many vacations will each student at Fallon take this summer? Lesson 2: Dot Plots Station​
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Do this station if you missed #2a or #4b or need extra practice 7. Stephen surveyed people on his basketball team to collect data for the statistical question “how many hours of exercise do you get per week?” The responses he received were: {21, 20, 18, 18, 20, 21, 16, 21}. Create a dot plot of this data. 8. There is a rainforest in Manaus Brazil. The average rainfall each month was recorded. If we round each amount to the nearest whole number of inches, the data is as follows: Month Jan Feb March April May June July Aug Sept Oct Nov Dec Inches 10 10 12 11 8 4 3 2 3 4 6 9 a. Use the table above to create a dot plot. b. Based on your dot plot, how much rainfall typically occurs in the Manaus rainforest? Lesson 3­5: Mean Station​
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Do this station if you missed #2b, 3, the mean in #4 or need extra practice 9. Stephen surveyed people on his basketball team to collect data for the statistical question “how many hours of exercise do you get per week?” The responses he received were: {21, 20, 18, 18, 20, 21, 16, 21}. Find the mean of the data to describe a typical amount of exercise the players get. 10. There is a rainforest in Manaus Brazil. The average rainfall each month was recorded. If we round each amount to the nearest whole number of inches, the data is as follows: Month Jan Feb March April May June July Aug Sept Oct Nov Dec Inches 10 10 12 11 8 4 3 2 3 4 6 9 a. Use the mean to find out how much rainfall typically occurs in the Manaus rainforest. 11. Is your mean a precise indicator of a typical value for your data distribution in #9? Why or why not? (Making a dot plot may help) 12. Is your mean a precise indicator of a typical value for your data distribution in #10? Why or why not? (Making a dot plot may help) Lesson 6: MAD Station​
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Do this station if you missed the MAD (or table) in #4 or need extra practice Find the mean absolute deviation for each data set. Round the MAD to the nearest tenth as necessary. 13. {12, 11, 13, 11, 13} mean ______________ mean absolute deviation (MAD) ________________ 14. {4, 8, 6, 7, 7, 5, 5} mean ______________ mean absolute deviation (MAD) ________________ 15. Gilbert ran a quarter mile with these times (rounded to the nearest minute): {3, 5, 2, 3, 5, 6} a. Find the mean and the MAD of the data distribution. b. Create a dot plot of the data set. Represent the MAD on the dot plot with vertical lines. c. Write a sentence to state what the MAD represents in this situation. 16. Samantha decided to calculate the MAD of the speed of the cars driving by on a busy highway. She watched the sign showing speed as the cars drove by. The next 5 cars speeds registered as follows: {65, 72, 76, 68, 79}. a. Find the mean and the MAD of the data distribution. b. Write a sentence to state what the MAD represents in this situation. Lesson 7: MAD Interpretation Station​
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Do this station if you missed #5 or need extra practice 17. Two math classes, Class 1 and Class 2, have a mean test average of 86%. Class 1 has a MAD of 3.2 and Class 2 has a MAD of 3.6. For which class is the mean a better indicator of a “typical” test score for this data? State how you know and be specific. 18. A lemonade stand was open for a week. Each day they recorded how many lemonades they sold. At the end the average number of lemonades sold was 10. If the MAD is 1.5, write a sentence to state what the MAD represents for the lemonade sales. (HINT: Use lesson 7 notes) 19. An ice cream shop watched how many scoops of ice cream they sold each hour for an 8 hour period. The mean number of ice cream scoops per hours was 5.3 scoops. If the MAD is 2.3, write a sentence to state what the MAD represents for the number of ice cream scoops sold. CHALLENGE: 20. The following represents the data distribution from the statistical question “how many hours of tv/computer do 6th graders typically use on a school night at home?” {0, 1, 3, 3, 2, 2, 1, 6, 6, 2} a. Find the mean of the data distribution. b. Identify any outlier(s) in the data distribution. Include a description of what an outlier is. c. Find the mean of the data distribution if we do not include the outlier(s). d. How did including the outlier(s) affect the mean? e. Plot the data distribution on a dot plot. Describe the shape of the data. f. How does the shape also give a hint to show how the outlier(s) affect the mean? 21. As we have learned in previous lessons, the mean is a good/precise measure of a typical value (the center) if there is low variability around the mean (small MAD). As you explored in the problem above, having outliers increases the variability of a data distribution and can affect your mean (by pulling it higher or lower), making it not as typical or precise to describe the entire data distribution. In cases like this when the data is skewed left or skewed right another measure of center called the ​
median​
can be more precise to measure a typical value. Follow the steps below to practice finding the ​
median​
(lesson #8 coming soon!). a. The number of times a class typically has won Friday Trivia during the announcements has been collected for 9 sixth grade classrooms: {12, 10, 10, 11, 11, 16, 18, 10, 11}. i.
STEPS: 1. To find the ​
median​
, first order the data from least to greatest. 2. Next, starting on each end, count one data at a time to get to the middle. Because there is an odd number of numbers, when you count to the middle you will be left with one number. The very middle number is your ​
median. ​
The median is just the center number in an ordered list of numbers. ii.
What is the median of this data? iii.
Find the mean. iv.
Are there any outlier(s) in this data that may be affecting the mean? If so, list them and describe how they are affecting the mean. b. Suppose one more class included their data in this distribution. Now with 10 classes the data is: {12, 10, 10, 11, 11, 16, 18, 10, 11, 12}. i.
STEPS: 1. To find the ​
median​
, first order the data from least to greatest. 2. Next, starting on each end, count one data at a time to get to the middle. Because there is an even number of numbers, there are two numbers in the middle. We need to find the middle of these numbers. In other words, we have to find the MEAN of the 2 numbers in the middle. This will find their exact center. ii.
What is the median of this data? 22. Practice. Find the median of each set of data below. a. Number of Monkeys at different zoos: {28, 18, 36, 42, 18, 34, 25, 16, 12, 30, 44} b. Dina’s test scores: {93, 85, 88, 97, 94, 90, 93} c. Costs of juice: {1.65, 1.97, 2.45, 2.87, 2.35, 3.75, 2.49, 2.87} d. Average Speeds (mph): {40, 52, 44, 46, 52, 40, 44, 50, 41, 44, 44, 50}