What is the association of between the two variables? In what direction does the association go?

Transcription

1 Common Core Standard: 8.SP.4 What is the association of between the two variables? In what direction does the association go? How strong is the association between the two variables? CPM Materials modified by Mr. Deyo

2 Title: IM8 Ch What If The Data Is Not Numerical? Date: Learning Target By the end of the period, I will describe associations between two categorical variables in two way tables and explain how an association can be seen in table rows or in table columns. I will demonstrate this by completing Four Square notes and by solving problems in a pair/group activity.

3 Home Work: Sec Desc. Date Due Review & Preview 3 Problems: 7 111, 7 112, 7 115

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5 1) association Vocabulary 2) direction of association 3) strength of association 4) outliers

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7 7.3.3 What If The Data Is Not Numerical? In previous lessons, you described the association between two numerical variables, such as the amount of fertilizer used and the height of the plant. Some variables, however such as gender, eye color, names of countries, or weather conditions are not numerical. Since the data are in categories, non numerical variables are called categorical variables. Another type of categorical variable occurs when numerical variables are lumped into categories, such as in age groups. Today you will look for relationships in variables that are not numerical. As you work with your study team today, keep the following questions in mind: What is the association of between the two variables? In what direction does the association go? How strong is the association between the two variables?

8 The experiments students did with plants and different growing conditions in Lesson caught the attention of a local farmer. He was interested in whether the type of soil made a difference in the height of his corn crop. He planted 2500 stalks of corn and collected the following data. This type of table is called a frequency table because it shows counts, or frequencies, in each of the cells of the table. a) Make a conjecture about the effect of soil type on the height of the corn. b) The table of data on corn height used counts because it counted the number of stalks of corn. When analyzing categorical data, percents are much easier to analyze. But first, you need to determine the independent variable so that you can determine, Percent of what? What is the independent variable in this situation? c) Create a second table that contains the data above but as percentages instead of counts. The percentage should be the count for each height category out of the total number for that soil type. For example, the height of the bar for 0 3 ft will be 9.0%, because is The third row of the table is not needed in this case. Height of Corn (ft) Sandy Soil Clay Soil Total % % 0 3 ft % 3 4 ft % 4 6 ft % 7 8 ft Total %

9 7 108a,b. The farmer is interested in the height of his corn for each of the two soil types. A straightforward way to compare the effect of the independent variable is to make a different bar graph for each independent variable. a) Make a bar graph for the SANDY soil. The horizontal axis should be the height categories. The vertical axis will represent the percent of the corn in sandy soil that grew to that height. b) Make a similar bar graph for the other independent variable (CLAY). % of Height of SANDY Soil Corn (ft) % 0 3 ft % 3 4 ft % 4 6 ft % 7 8 ft % of Height of CLAY Soil Corn (ft) % 0 3 ft % 3 4 ft % 4 6 ft % 7 8 ft

10 7 108c,d. The farmer is interested in the height of his corn for each of the two soil types. A straightforward way to compare the effect of the independent variable is to make a different bar graph for each independent variable. c) Is the height of corn associated with the soil type? That is, does the soil type have an impact on height? Report your conclusions to the farmer. d) Why did you make a bar graph instead of a histogram for the height of the corn?

11 7 109a,b. The nutrition staff at CPM Diabetic Institute is interested in the impact of three new energy bars on blood sugar levels. The staff conducted a study on 1000 volunteers and collected the following data. TOTAL TOTAL a) Complete the table by computing row and column totals. What is the independent variable? b) A relative frequency table displays the percents in a table instead of a bar graph. Change the frequency table at the beginning of this problem to a relative frequency table by changing the counts to percents. For example, the 30 Mighty Bars that lowered blood sugar will be displayed as 20%. Lower Blood Sugar % Mighty Bar % Force Bar % Strength Bar Higher Blood Sugar

12 7 109c. The nutrition staff at CPM Diabetic Institute is interested in the impact of three new energy bars on blood sugar levels. The staff conducted a study on 1000 volunteers and collected the following data. c) Use your data from the relative frequency table to make a bar graph for each of the independent variables. The horizontal axis should be the dependent variable. Lower Blood Sugar % Mighty Bar % Force Bar % Strength Bar Higher Blood Sugar % Mighty Bar % Force Bar % Strength Bar d) Is there an association between blood sugar level and the choice of energy bar?

13 An unusually severe increase in gasoline prices may have motivated full sized pickup truck buyers to purchase a highly fuel efficient vehicle. Purchase behavior was collected in one area for one year and reported below. chapter/ch7 TOTAL TOTAL a) Complete the row and column totals. What is the independent variable? b) Create a relative frequency table. Is there an association between fuel prices and the number of highly fuel efficient trucks purchased? % Highly Fuel Efficient Trucks Purchased % Low Fuel Prices % High Fuel Prices % Ordinary Cars & Regular Trucks Purchased

14 Researchers have determined that teenagers memories are negatively affected by getting less than 10 hours of sleep. Being good scientists, the math students at North Middle School were skeptical, so they did their own study. They asked 300 students to memorize 10 objects. The next day, each student was asked how much sleep he or she got and then was asked to list the ten items. home chapter/ch7/lesson/7.3.3/problem/7 Make a relative frequency table to determine if there is an association between hours of sleep and memory. Remembered ALL 10 Items % Yes % No % Less than 7 hours sleep % 7 9 hours sleep % At least 10 hours sleep

15 Ruthie did a survey among her classmates comparing the time spent playing video games to the time spent studying. The scatterplot of her data is shown here. chapter/ch7/lesson/7. a) What association can you make from her data? b) Use an ordered pair (x, y) to identify any outliers. (, ) (, )

16 Sao can text 1500 words per hour. He needs to text a message with 85 words. He only has 5 minutes between classes to complete the text. Can he do it in 5 minutes? homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.3.3/problem/7 113

17 Where would the point (11, 18) be after each transformation described below? homework/home chapter/ch7/lesson/7.3.3/problem/7 114 a) Reflect (11, 18) across the x axis, and then reflect that point across the y axis. (, ) b) Translate (11, 18) 5 units to the right and 3 units down. (, )

18 7 115a. This problem is a checkpoint for solving equations with fractions and decimals (Fraction Busters). It will be referred to as Checkpoint 7. Solve each equation or system of equations. 1x 1x = homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.3.3/problem/7 115

19 7 115b. This problem is a checkpoint for solving equations with fractions and decimals (Fraction Busters). It will be referred to as Checkpoint 7. Solve each equation or system of equations. homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.3.3/problem/7 115 x x = $2

20 7 115c. This problem is a checkpoint for solving equations with fractions and decimals (Fraction Busters). It will be referred to as Checkpoint 7. Solve each equation or system of equations. homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.3.3/problem/7 115 x+2 = x 2 3 7

21 7 115d. This problem is a checkpoint for solving equations with fractions and decimals (Fraction Busters). It will be referred to as Checkpoint 7. Solve each equation or system of equations. 2x y = homework/homework/category/cc/textbook/cc3/ chapter/ch7/lesson/7.3.3/problem/7 115 y = 1x