FOA/Algebra 1 Unit 6: Describing Data Notes Unit 6 .

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FOA/Algebra 1Unit 6: Describing DataNotesUnit 6: Describing DataAfter completion of this unit, you will be able to Learning Target #1: Data Analysis Construct appropriate graphical displays (dot plots, histograms, and box plots) to describesets of data. Select the appropriate measures to describe and compare the center and spread of two ormore data sets. Use the context of the data to explain why its distribution takes on a particular shape. Explain the effect of outliers on the shape, center, and spread of the data sets.Learning Target #2: Frequency Tables Create two way frequency tables from a set of data on two categorical variables Calculate joint, marginal, and conditional relative frequencies and interpret in context. Recognize associations and trends in data from a two way table.Learning Target #3: Regression Models Create and interpret a scatterplot Interpret the correlation coefficient Discuss the differences between correlation and causation Determine which type of function best models a set of data Interpret constants and coefficients in the context of the data. Use the function model to make predictions and solve problems in the context of the dataTimeline for Unit 6Monday16Tuesday1723Day 5:Frequency Tables30Day 1:CalculatingMeasures ofCentral Tendency& Spread24Day 6:Associations withConditionalFrequencies1EOC ReviewWednesday18Day 2:Dot Plots andHistogramsBox Plots25Day 3:Comparing DataSetsDay 7:Interpret LinearModels, Line ofBest FitDay 4:Changing of thechairs27Day 8:Unit 6 Review3EOC ReviewFriday20262EOC ReviewThursday19Day 9:Unit 6 Test4EOC TestEOC Test

FOA/Algebra 1Unit 6: Describing DataNotesDay 1 - Calculating Measures of Central Tendency & SpreadIn middle school, you learned how to calculate measures of central tendency (mean, median, mode). In thisunit, we are going to use measures of central tendency, along with other statistical concepts to describe dataspreads. Before we review measures of central tendency, it is important to understand the types of data wewill be using.Types of DataThere are several different classifications of data: univariate versus bivariate, categorical versus quantitative.Univariate dataBivariate dataInvolves a single variableInvolves two variablesDoes not deal with causes and relationshipsDeals with causes and relationshipsPurpose is to describe dataPurpose is to explain dataTypes of data calculations: mean, median, mode,range, mean absolute deviation, quartiles, bargraphs, histograms, box plots, dot plotsTypes of calculations: correlations, comparisons,relationships, cause and effect,independent/dependent variables,Example: Travel time (minutes): 15, 29, 8, 42, 35, 21,18, 42, 26Example: An ice cream shop keep tracks of howmuch ice cream they sell versus the temperature onthat day.Example Question: How many of the students in thefreshman class are female?Example Question: Is there a relationship betweenthe number of females in computer programmingand their scores in mathematics?Categorical – Places an individual into one of several groups or categories (gender, hair color, eye color, etc)Quantitative – Numerical values (test scores, age, grade point average, etc)Classify: Classify the following as either categorical or quantitative data:a. Marital statusb. A person’s heightc. Hair Colord. # of Children in a Family

FOA/Algebra 1Unit 6: Describing DataNotesMeasures of Central TendencyMeasures of Central Tendency are used to generalize data sets and identify common values.Definition: Average of a numerical data set, denoted as xMeanCalculation: Add up all the data values and divide by the number of data valuesUseful When: - Data values do not vary greatly- No outliers- Distribution is symmetricExample: Find the mean of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22Definition: The middle number when the values are written in numerical orderMedianCalculation: Rewrite your data values in numerical order to find the middle number.o If your data set is ODD, then the median will be the number that fallsdirectly in the middle.o If your data set is EVEN, then the median is the average of the twomiddle numbers.Useful When: - Distribution is skewed- Data values contain an outlierExample: Find the median of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22First andThirdQuartilesDefinition: Quartiles are values that divide a list of numbers into quarters First (Q1) Quartile: Median of the lower half of a data seto Calculation: Find the middle number of the values to the left of the median Third (Q3) Quartile: Median of the upper half of a data seto Calculation: Find the middle number of the values to the right of the medianExample: Find the lower and upper quartiles of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22

FOA/Algebra 1Unit 6: Describing DataModeDefinition: Value that occurs most frequently. There can be no, one, or several modesNotesCalculation: Find the numbers that are repeatedo NO MODE (No numbers repeat) Say “no mode”o ONE MODE (One number repeats) State the number that repeatso MORE THAN ONE MODE (Several numbers repeat the same amount oftimes) State the numbers that repeat.Useful When: - Data set contains categorical dataExample: Find the mode of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22OutliersData value that is much greater than or much less than the rest of the data in a data setIf an outlier is present, you would use the median to describe the data, NOT the mean!Example: Identify any outliers in the data set. Then determine if the median or mean best represents the datasets.a. 15, 10, 12, 18, 10, 22b. 128, 152, 170, 41, 161Measures of SpreadMeasures of Spread describe the “diversity” of the values in a data set. Measures of spread are used to helpexplain whether data values are very similar or very different.Definition: Difference between the greatest and least values in the setRangeCalculation: Subtract the smallest data value from the biggest data valueRange Biggest # - Smallest #Example: Find the range of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22

FOA/Algebra 1InterquartileRange (IQR)Unit 6: Describing DataNotesDefinition: The difference between the third and first quartiles (Q3 – Q1). It finds the distancebetween two data values that represent the middle 50% of the data.Calculation: Subtract the first quartile value from the third quartile value (Q 3 – Q1).Example: Find the interquartile range of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22MeanAbsoluteDeviationDefinition: Average absolute value of the difference between each data point and themean. It essentially takes the average distance of the data points from the mean.A data set with a smaller mean absolute deviation has data values that are closer to themean than a data set with a great mean absolute deviation. The greater the mean absolutedeviation, the more the data is spread out.X1 data valueThe formula for mean absolute deviation is:x mean sumN number of data valuesCalculation: -Find the mean of the set of numbers- Subtract each number in the set by the mean and take the absolute valueof each new number (new number will be positive)- Find the sum of the new numbers and divide by the number of data valuesExample: Find the MAD of the following numbers.a. 76 77 79 80 82 88 90 92 95b. 15, 10, 12, 18, 10, 22

FOA/Algebra 1Unit 6: Describing DataNotesPutting Measures of Center and Spread TogetherUse the data set below to answer the following questions:5, 2, 9, 10, 3, 7, 2, 18, 12, 15, 1, 6, 9, 5, 2, 71.) Find the mean.2.) Find the median(Q2).3.) Find the mode.4.) Find the range.5.) Find Q1.6.) Find Q3.7.) Find the IQR.8.) Find the MAD.

FOA/Algebra 1Unit 6: Describing DataNotesDay 2 - Dot Plots & HistogramsA dot plot is a data representation that uses a number line and x’s, dots, or other symbols to show frequency.The number of times a value is repeated corresponds to the number of dots above that value. A dot plot alsoshows the size of the data set. Dot plots are also called line plots. An example of a dot below is vantages of Dot Plots:Simple to makeShows each individual data pointDisadvantages of Dot Plots:Can be time consuming with lots of data pointsHave to count to get exact totalFractions are hard to displayTypes of Dot Plot DistributionsTYPEDESCRIPTIONWhen graphed, a vertical line drawn at thecenter will form mirror images.SYMMETRICThis shape is referred to as the bell shapedcurve or normal curveMean is approximately equal to the medianSKEWED LEFT(NEGATIVESKEW)SKEWED RIGHT(POSITIVESKEW)Fewer data points are found to the left ofthe graph (towards the smaller data values).The “tail” of the graph is to the left.Typically, the mean is less than or to the leftof the median.Fewer data points are found to the right ofthe graph (towards the bigger data values).The “tail” of the graph is to the right.Typically the mean is greater than or to theright of the medianThe data is spread equally (or very close toequally) across the range.UNIFORMUniform distributions are a type of symmetricdistributions.Practice 1: Identify the type of distribution of the following dot plots.PICTURE

FOA/Algebra 1a.Unit 6: Describing Datab.NotesPractice 2: Find the following values:Describe the tion:Distribution:Practice 3: The following dot plot represents gold medals won at the Special Olympics:

FOA/Algebra 1Unit 6: Describing Dataa. How many participants are represented in the dot plot?b. How many participants won10 or more medals?c. How many participants won less than 4 medals?d. Describe the data distribution and interpret its meaning in terms of this problem situation.Notes

FOA/Algebra 1Unit 6: Describing DataNotesHistogramsA histogram is a bar graph used to display the frequency of data divided into equal intervals, called bins. Thebars must be of equal width and should touch, but not overlap. The height of each bar gives the frequency ofthe data.An example of a histogram is below:How many students read 4-7 books?How many more students read 4-7 books than 12-15 books?Advantages of Histograms:Good for determining the shape of dataConvenient for representing large quantities of dataDisadvantages of Histograms:Cannot read exact values because data is grouped into categoriesMore difficult to compare two data sets because measures of center andspread cannot be determinedTYPESYMMETRICDESCRIPTIONWhen graphed, a vertical line drawn at the centerwill form mirror images.This shape is referred to as the bell shaped curve ornormal curveThe median will be in or close to the center of thenumber line.SKEWED LEFT(NEGATIVESKEW)SKEWED RIGHT(POSITIVESKEW)Fewer data points are found to the left of the graph(towards the smaller data values). The “tail” of thegraph is to the left.The median will be shifted right and the “tail” on theleft. Typically, the mean is less than or to the left ofthe median.Fewer data points are found to the right of thegraph (towards the bigger data values). The “tail”of the graph is to the right.The median will be shifted left and the “tail’ on theright. Typically the mean is greater than or to theright of the medianThe data is spread equally (or very close to equally)across the range.UNIFORMUniform distributions are a type of symmetricdistributions.The median will be in or close to the center of thenumber line.PICTURE

FOA/Algebra 1Unit 6: Describing DataNotesPractice 1: Describe the distribution of each histogram and if the mean is less, greater, or equal to the median.Then describe which would be a better measure of center; the median or mean.a.b.Practice 2: Use the histogram to answer the following questions about how long it takes students to get ready.a. How many students answered the question?b. How many students take less than 40 minutes to get ready?c. Based on the info given, could you redraw the current histogram withintervals half their current size? Why or why not?Practice 3: Analyze the given histogram which displays the ACT composite score of several randomly chosenstudents.a. Describe the distribution and explain what it means in terms of theproblem situation.b. How many students had an ACT score of at least 20?c. How many students had an ACT score less than 30?d. How many students had an ACT score of exactly 25?

FOA/Algebra 1Unit 6: Describing DataNotesDay 3 - Box PlotsA box plot (also called box and whisker plot) is used to show how data values are distributed. They are createdusing five important numbers that show the minimum, maximum, median, lower quartile, and upper quartile.In a box plot, a rectangle is drawn starting at the first quartile and ending at the third quartile. The rectangleshows the middle 50% of the data set. The median is represented by a line. Whiskers are drawn from therectangle to the minimum and maximum data values. An example of a box plot is below:Types of Box Plot DistributionsTYPEDESCRIPTIONWhen graphed, a vertical line drawn at the centerwill form mirror images.SYMMETRICThis shape is referred to as the bell shaped curve ornormal curveSKEWED LEFT(NEGATIVESKEW)SKEWED RIGHTPICTUREThe median and mean will be approximately equal.Fewer data points are found to the left of the graph.The “tail” of the graph is to the left.The interquartile range will be shifted to the right ofthe number line (inside IQR) and the mean less thanthe median.Fewer data points are found to the right of thegraph. The “tail” of the graph is to the right.(POSITIVESKEW)The interquartile range will be shifted to the left ofthe number line and the mean greater than themedian.The data is spread equally (or very close to equally)across the range.UNIFORMUniform distributions are a type of symmetricdistributions.The median and mean will be approximately equal.Outliers: A data value that lies on the outside of all the other data values. It is denoted by an asterisk (*) or dot.

FOA/Algebra 1Unit 6: Describing DataNotesIdentifying DistributionsIdentify the type of distribution of the following box plots.a.b.c.Calculating the Parts of a Box PlotBefore you can even create a box plot, you have to know how to calculate the “five number summary”, whichconsists of the minimum, maximum, median, lower quartile, and upper quartile.Using the following data set, find the five number summary:{15, 10, 12, 18, 10, 22, 11, 17, 13}Minimum: Smallest number of the data setMaximum: Largest number of the data setMedian: Middle number of the data setLower Quartile: Median of the lower half of the data set (Q1 or First Quartile)Upper Quartile: Median of the upper half of the data set (Q3 or Third Quartile)

FOA/Algebra 1Unit 6: Describing DataNotesInterpreting Box PlotsList the data values that fall below 25%:List the data values that fall above 75%:List the data values that fall above 50%:Calculate the IQR:Practice with Box PlotsExample 1: Analyze the box plot below about the cost, in dollars, of 12 CD’s. Answer the questions.A. Which cost is the upper quartile?B. What is the range?C. What is the median?D. Which cost represents the 100th percentile?E. How many CD’s cost between 14.50and 26.00?F. How many CD’s cost less than 14.50?

FOA/Algebra 1Unit 6: Describing DataExample 2: Analyze the box plot below and answer the following questions:A. What is the height range of the middle50 percent of the surveyed adults?B. How many of the surveyed adultsare between 72 and 79 inches?C. What percent of the surveyed adultsare 72 inches or shorter?D. What is the height of the tallestadult surveyed?E. About 10 people have a height below whatamount?F. About 20 people have a heightabove amount?G. How many of the surveyed adults areat least 58 inches tall?H. Describe the distribution. Is the medianor mean best describe the data?Notes

FOA/Algebra 1Unit 6: Describing DataNotesExample 3: Jamie has organized the amount of sugar, per serving, in many different cereals and created a boxplot of his data below:a. State the numbers (including what they represent) for the five number summary.b. Give three conclusions that can be made about the sugar amount in one serving of breakfast cereal.c. Describe the distribution and interpret the meaning of the distribution in terms of this problem situation.d. Jamie says that more breakfast cereals have over 10 grams of sugar per serving than have under 5 grams ofsugar per serving because the whisker connecting Q3 to the maximum is longer than the whisher connectingQ1 to the minimum. Is he correct? Explain why or why not.

FOA/Algebra 1Unit 6: Describing DataNotesDay 4 – Comparing Data SetsScenario: Coach Smith is trying to decide which two of his point guards he wants to start for the first round ofplay-offs. The data below shows the numbers of points scored by Jace and Tyler from the past six games.Jace: 11, 11, 6, 26, 6, 12Tyler: 15, 12, 13, 10, 9, 131. Who do you think Coach Smith should select as a starting player and why?2. What is the mean for Jace:Tyler: ?3. Calculate the deviations for the points scored for each player. Then describe the deviation.JacePoints ScoredDescribe DeviationTylerPoints Scored111511126132610691213Describe DeviationWhat do you notice about the deviations for each player?4. Add the deviations for each player and divide by the number of data values.JaceTyler5. What does the mean absolute deviation tell you about the points scored by each player?6. If you were Coach Webb, which player would you choose to start in the play-off game and why?

FOA/Algebra 1Unit 6: Describing DataNotesComparing Measures of Center and SpreadCenterMeanMedian Comparing Measures of Center and SpreadSpreadData is SymmetricNo Outliers Skewed Data Outliers(Skewed left – mean median)(Skewed right – mean median) More Spread Less Spread Data values are spreadoutGreater MADData values are closetogetherSmaller MADExample 1: Which data set will have the greater mean absolute deviation? Why?Example 2: The following data represents test scores from Unit 11 test.Unit 11 Test Scores: 81, 41, 89, 92, 80, 86, 77, 66, 84, 92, 97, 88, 77, 38a. Compare the mean and median.b. What type of distribution does the data create? What does this mean?c. Are there any outliers?d. What measure of center best describes the grades and why?

FOA/Algebra 1Unit 6: Describing DataNotesExample 3: The histograms below show the scores of Mrs. Smith’s first and second block class at Red Rock HighSchool.1. How many students are in her 1st and 2nd block class?2. How many students failed the test in each class?3. Which measure of center best describes the data and why?4. Which class seemed to do better overall?

FOA/Algebra 1Unit 6: Describing DataNotesExample 4: Each girl in Mrs. Washington’s class and Mrs. Wheaton’s class measured their own height. Theheights were plotted on the dot plots below. Use the dot plots to compare the heights of the girls in the twoclasses.Mrs. WashingtonMrs. Wheatona. Describe the distribution for each class.c. What is the mean and median for each class?b. Which teacher’s girls appear to be taller and why?d. How tall are the majority of the girls in eachclass?Example 5: The following box plots show the average monthly high temperatures for Milwaukee and Honolulu.Use the box plots to answer the following questions.HonoluluA. What was the median temperature for both cities?C. Which city has more spread in its data and why?D. Interpret what the 1st and 3rd quartiles mean for both cities.MilkwaukeeB. What was the range for both cities?

FOA/Algebra 1Unit 6: Describing DataNotesDay 5 – Frequency TablesA relative frequency is the frequency that an event occurs divided by the total number of events.Example: If your team has won 9 games from a total of 12 games played:The frequency of winning is 9The relative frequency of winning is 9/12 75%.A two way table is a useful way to organize data that can be categorized by two variables (bi-variate). Thefollowing table shows the results of a poll of randomly selected high school students and their preference foreither math or English. Joint frequencies are the number of times a response was given for a certaincharacteristic. Marginal frequencies is the total number of times a response is given for a certain characteristic.Marginal frequencies are found in the margins of the table.MathEnglish9th Total1. How many students are in 11th grade?2. How many students are in 9th grade and prefer math?3. How many students prefer English and are in 12th grade?4. How many students are there total?Example 1: Fill in the missing values into the table below and then answer the following questions:9th Grader’s School Transportation Surveya. How many students are there total?b. How many 9th boys walk to school?c. How many 9th girls ride their bike to school?d. How many males took the survey?

FOA/Algebra 1Unit 6: Describing DataNotesExample 2: The table below represents the favorite meals of 9th and 10th graders. Use the table to answer thefollowing questions.a. How many 9th graders participated in the survey?b. How many students prefer chicken nuggets?c. How many students prefer burgers?d. Which meal is the least favorite of all students?e. Which meal is the least favorite of 9 th graders?f. Which meal is most favorite of 10th graders?Joint and Marginal Relative FrequenciesThe joint relative frequencies are the values in each category divided by the total number of values and writtenas percents (or decimals). They provide the ratio of occurrences in each category to the total number ofoccurrences.The marginal relative frequencies are found by adding the joint relative frequencies in each row and column(totals) and are written as percents (or decimals). They provide the ratio of total occurrences for each categoryto the total number of occurrences. Marginal frequencies are written in the MARGINS of the table. The marginalfrequency totals in each row and column should always total 1 or 100%.Calculate the joint and marginal relative frequencies for the table:9th Grade10th Grade11th Grade12th GradeMathEnglishTotala. What percent of students are 10th graders & like English?b. What percent of students like Math and are 12th graders?c. What percent of students like Math?d. What percent of those surveys were seniors?Total

FOA/Algebra 1Unit 6: Describing DataNotesPractice with Joint and Marginal Relative FrequenciesExample 3: One hundred people who frequently get migraine headaches were chosen to participate in astudy of new anti-headache medicine. Some of the participants were given the medicine; others were not.After one week, the participants were asked if they got a headache during the week. The two way frequencytable summarizes the results. Fill in the missing value and then create a joint and marginal relative frequencytable.Did NOT TakeTook MedicineTOTALMedicineHeadache12No Headache48TOTAL272540Joint and Marginal FrequenciesTook MedicineDid NOT TakeMedicineTOTALHeadacheNo HeadacheTOTALExample 4: Create a joint and marginal relative frequency table to represent the favorite movies of students.a. What percent of people prefer towatch comedies?b. What percent of people prefer towatch horror movies?c. What percent of people are from classA and prefer to watch drama movies?d. Which class prefers watching horrormovies?

FOA/Algebra 1Unit 6: Describing DataNotesConditional FrequenciesA conditional frequency is restricted to a particular group (or subgroup). Conditional frequencies are typicallyidentified by the words “given that” or “if” or “what percent of (insert condition)”. They do NOT come from thetotal data, but from a row or column total. To calculate a conditional frequency, divide the joint relativefrequency by the marginal relative frequency (does not matter if they are the frequencies orpercents/decimals). Conditional frequencies are used to find conditional probabilities.Took MedicineDid NOT TakeMedicineTOTALHeadache121527No Headache482573TOTAL60401001. What is the probability that a participant did not get a headache if they took the medicine?2. What is the probability that a participant took medicine given they did not have a headache?3. What is the probability that a participant took medicine given they did have a headache?4. Calculate the joint and marginal frequencies from the table above.Did NOT TakeTook MedicineMedicineTOTALHeadacheNo HeadacheTOTAL5. What is the probability that a participant who did not get a headache took the medicine?6. What is the probability that a participant took medicine given they did not have a headache?7. What is the probability that a participant took medicine given they did have a headache?8. What do you notice about the answers from problems 1 – 3 and problems 5 – 7?

FOA/Algebra 1Unit 6: Describing DataNotesExample 5: Students were surveyed about whether or not they have a pet and if they are allergic or not toanimals. The results are below:a. What percent of those surveyed who are allergic to animals have a pet?b. What percent of those surveyed who are not allergic to animals have a pet?c. What percent of those who have a pet are allergic to animals?d. What percent of those who have a pet are not allergic to animals?Example 6: The following contains the scores of the latest math project. Use the table to answer the followingquestions:a. What percentage of males earned a score of an “A”?b. What percentage of those who earned an “A” were male?c. What percentages of females earned a score of a “B”?d. What percentage of those who earned an “F” were female?

FOA/Algebra 1Unit 6: Describing DataNotesDay 6 - Associations with Conditional Relative FrequenciesScenario: Mr. Lewis teaches three science classes at South Creek High School. He wants to compare thegrades of the three classes of his students. He created a frequency chart as shown below:a. Create a joint and marginal relative frequency chart below:b. Which class is his biggest?c. What percent of his students earned an A?d. What percent of his Chemistry students earned a B?e. Which class did the best overall? Why?

FOA/Algebra 1Unit 6: Describing DataNotesBecause each science class has a different number of students, the relative frequencies cannot helpdetermine which class is doing the best. Instead, we need to use a conditional relative frequency chart todetermine which class did the best. A conditional relative frequency chart is the percent or ratio of occurrenceof a category given a specific value of another category. For example, what percent of his Biology studentsearned an A? If I calculate this, I am only going to take the number of occurrence of getting an A for thenumber of biology students only (6 students got an A in biology out of 20 biology students).f. Create a conditional relative frequency table below:Answer the following and consider passing as earning only an A, B, or C.g. What percent of biology students are passing?h. What percent of chemistry students are passing?i. What percent of physics students are passing?j. Which science class is doing the best according to their grades?

FOA/Algebra 1Unit 6: Describing DataNotesThe differences in conditional relative frequencies can be used to assess whether or not there is an associationbetween two categorical variables. The greater the difference in the conditional relative frequencies, thestronger the evidence lies that an association exists. An observed association between two variables does notnecessarily mean that there is a cause and effect relationship between the two variables. Take a look at thefollowing scenario below:Example 1: The following table surveyed students about their homework completion and skipping class.a. What do you notice between skipping class and doing homework?b. Does there seem to be an association between doing homework and skipping class?Example 2: The conditional relative frequency table shown below shows the sports that females and malestudents participate in. Is there an association between your gender and the sport you choose to play?

FOA/Algebra 1Unit 6: Describing DataNotesExample 3: The table below shows the frequencies of having a sports car and running regularly. Use the tableto answer the following questions.a. What percent of people who have a sports car also run regularly?b. What percent of people who do not run regularly do not own a sports car?c. Create a conditional relative frequency chart below.Has a Sports CarDoes Not have aSports CarTotalRuns RegularlyDoes Not RunRegularlyTotald. Does there appear to be an association between having a sports car and running regularly? Why or whynot?

FOA/Algebra 1Unit 6: Describing DataNotesExample 4: Students were given the opportunity to prepare for a college placement test in mathematics bytaking a review course. Not all students took advantage of this opportunity. The following results wereobtained from a random sample of students who took the placement test.a. What percent of the students took the review course?b. What percent of students placed in math 200?c. What percent of students who took the review course placed in Math 50?d. What percent of students who placed in math 200 did not take the review course?e. Create a conditional relative frequency chart below.Placed in Math200Placed in Math100Placed in Math 50TotalTook ReviewCourseDid Not TakeReview CourseTotalf. Is there an association between taking the review class and placing in a math class? Why or why not?

FOA/Algebra 1Unit 6: Describing DataNotesDay 7 – ScatterplotsA scatterplot is a graph of data pairs (x, y). Scatterplots are typically used to describe relationships, calledcorrelations, between two variables (bi-variate). The correlation coefficient de

mean than a data set with a great mean absolute deviation. The greater the mean absolute deviation, the more the data is spread out. The formula for mean absolute deviation is: Calculation: - Find the mean of the set of numbers - Subtract each number in the set by the mean and take the absolute

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