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NC.M1.S-ID.1 Use technology to represent data with plots on the real number line (histograms and box plots).NC.M1.S-ID.2 Use statistics appropriate to the shape of the data distribution to compare center (median, mean) and spread (interquartile range, standard deviation) of two or more different data sets. Interpret differences in shape, center, and spread in the context of the data sets.NC.M1.S-ID.3 Examine the effects of extreme data points (outliers) on shape, center, and/or spread.Create a frequency table and histogram of the data provided by your classmates. Use intervals of ten starting with 0-9.Average amount of time (in mins) of your ride to school:35, 15, 30, 55, 3, 10, 15, 15, 5, 3, 9, 5, 5, 4, 15, 50, 20, 30Several teachers were surveyed to see how long it takes them to drive to school. Average amount of time (in minutes) of your drive to school: 5, 8, 6, 26, 10Determine the meanMedianIQRStandard deviation QUOTE Which better represents the data set, mean or median? Justify your answer. Below are the measurements, in inches of the heights of students in one class. MaleFemale606262635860506651586253646350595761636458677461Create a frequency table (intervals of 3 – starting with 50-52, 53-55…) for EACH set of data. Create a histogram (same intervals) for EACH set of data.Create a back to back box plot for the two sets of data. Calculate:StatisticMale Female QUOTE (Mean)Range QUOTE (Standard Deviation)Min Q1MedianQ3MaxIQR (Inter-Quartile Range)OutliersDescribe the Male data in context.Does mean or median best describe the Male data? Explain. Describe the Female data in context.Does mean or median best describe the Female data? Explain. Compare and contrast both data sets.Below are the monthly temperatures for Dallas Texas in two different years. Use the data below to answer the questions. Average Monthly Temperature in Dallas Texas in 201250.452.564.370.377.984.387.786.580.067.059.751.2Average Monthly Temperatures in Dallas Texas in 197822.149.457.266.877.484.187.184.981.666.756.447.6a) Create a histogram (with intervals of 15, starting at 20) for each set of data:20121978b) Describe the 2012 Dallas Texas Temperature data in context.c) Describe the 1978 Dallas Texas Temperature data in context.d) Compare and contrast the 1978 and 2012 Dallas Texas Temperature Data sets.Suppose you are the leader of your group and you must explain the following questions in a way such that everyone at your group understands the topics you are studying! Explain what Standard Deviation is and why it’s used. Give details and examples to support your explanation.Explain the difference between Mean and Median and how to determine which is used to describe sets of data. Give details and examples to support your explanation.Students in a CCMI class were asked how long it takes to ride to school each morning.The girls in the class had the following responses (in minutes): 3, 15, 18, 38, 13, 20, 75, 5, 5, 30.The boys in the class had the following responses (in minutes): 50, 5, 20, 25, 20, 5, 30, 3, 8, 13Using the above data, answer the following questions:a) Create a histogram (with intervals of 10, starting at 0) for each set of data:Girls Ride TimeBoys Ride Timeb) Calculate for each set of data:StatisticGirls Ride TimeBoys Ride Time QUOTE (Mean)Range QUOTE (Standard Deviation)Min Q1MedianQ3MaxIQR (Inter-Quartile Range)OutliersHere is the formula for Standard Deviation in case you don’t want to let the calculator do it for you: QUOTE c) Create a side-by-side boxplot for the two sets of datad) Describe the Girls Ride Time data in context.e) Does mean or median best describe the Girls Ride Time data? Explain. f) Describe the Boys Ride Time data in context.g) Does mean or median best describe the Boys Ride Time data? Explain. h) Compare and contrast both data sets.i) Is Ride Time to School categorical data or quantitative data? Explain. On last week’s math test, Mrs. Smith’s class had an average of 83 points with a standard deviation of 8 points. Mr. Tucker’s class had an average of 78 points with a standard deviation of 4 points. Which class was more consistent with their test scores? How do you know? The data represents the number of texts sent by teachers per day:3, 15, 17, 17, 24, 35, 60Find the Five Number Summary for this set of dataDetermine the IQRDetermine if there are any outliers and prove your answer.Classify each of the following as categorical or quantitative data:1. Birth Year2. Number of books read3. Favorite genre of books4. Zip Code5. Shoe sizeDescribe the shape, center, and outliers of the data shown in the graphs below:Find the mean, median, mode, and range of the following set of numbers. Round to the nearest hundredth.60, 78, 82, 88, 88, 96, 97, 102, 102, 116, 120, 130, 210MeanMedianModeRange/SpreadCalculate the mean and median without the outlier. What affect did the outlier have on the mean and median-be specific.Would the mean or median best describe this data? Why?The two main uses for statistics are to ___________________ and to _____________________.“Measures of Center” or “central tendency” are ____________________ and _____________________.“Measures of Spread” include _________________, _____________________, and ______________.Jack wanted to know about how many pets everyone on his soccer team had. He recorded the number of pets his teammates had: 2, 5, 3, 6, 2, 4, 5, 1, 0. Find the minimum, maximum, range, median, and mean.Jill gathered data about how much time girls are spending in dance classes per week at her dance studio. The following amounts of time were recorded: 30 min, 45 min, 120 min, 40 min, 50 min, 35 min, 105 min, 25 min. Find the minimum, maximum, range, median, and mean.Determine whether the following variables are categorical (C) or quantitative (Q). Brand of vehicle purchased by a customerNumber of students in a class of 30 who prefer peanut M&M’s over plain M&M’sPhone number of all the students enrolled in schoolThe height of each player on the football teamThe amount of soda in a plastic bottleBrand of computer bought by a customerState of birth for each student in classPrice of a text bookThe zip codes of 150 studentsThe following are weights of book bags of students attending UNC: 2 lbs, 3lbs, 5 lbs, 6 lbs, 5 lbs, 37 lbs, 4 lbs, 3 lbs. Find the best measure of center for this dataset. Explain why the chosen measure of center is the best fit.A bank wants to improve its customer service. Before deciding to hire more workers, the manager decides to collect some information on the waiting times customers currently experience. During a week, customers were randomly selected, and their waiting times, in minutes, were recorded: 18.5, 9.1, 3.1, 6.2, 1.3, 0.5, 4.2, 5.2, 0.5, 10.8, 5.8, 1.8, 1.5, 1.9, 0.4, 3.5, 8.5, 11.1, 0.3, 1.2, 4.4, 3.8, 5.8, 1.9, 3.6, 2.5, 4.5, 5.8, 1.5, 0.7, 0.8, 0.1, 9.7, 2.6, 0.8, 1.2, 2.9, 3.0, 3.2, 2.8, 10.9, 0.1, 5.9, 1.4, 0.3, 5.5, 4.8, 0.9, 1.6, 2.2Construct a histogram using your calculator. Use a class size (interval) of 3.Sketch the histogram with proper labels. Describe the data distribution in context (remember the 4 different qualities)What is the window of the histogram you created?NCSU’s football scores for the 2012 season are as follows: 21, 10, 31, 52, 37, 17, 20, 35, 6, 37, 48, 27, 10, 47.Make a box plot of the points scored by NCSU’s football team in 2012.Make a frequency distribution table of the points scored by NCSU’s football team in 2012.Make a histogram of the points scored by the football team in 2012.Describe the data distribution in context (remember the 4 different qualities)An amusement park recorded the number of tickets sold daily for the month of May. The box plot shown below represents the data for the number of tickets sold, in hundreds.What percent did the amusement park sell more than 300 tickets per day?What is the median value of tickets sold per day?Joe interviewed the cross country team at his high school to find out how many miles per week they run. The following list is the data Joe collected. 15, 25, 33, 47, 52, 35, 6, 55, 42, 29, 45, 54, 41, 37, 48, 56, 45, 40 Create a box plot for the data set. Be sure to use the 1.5 IQR rule to determine if there are outliers. List the 5 number summary below the box plot.The table below shows the mean score and standard deviation of three middle schools’ football scores. Which football team is most likely to score the lowest in any given game? a. Mills Park Middle b. Davis Drive Middle c. East Cary MiddleSuppose that the two histograms above show the sleeping habits of the students at two different high schools. Wheatland High School is a small rural school consisting of 100 students while Urbandale High School is located in a large city and has 3,500 students.About what percent of the students at Wheatland get at least 8 hours of sleep per night?About what percent of the students at Urbandale get at least 8 hours of sleep per night?Which high school has more actual students that sleep between 9 – 10 hours per night?Which high school has a higher median sleep time?Explain which school’s students you think get more sleep as a whole. Back up your answer by referring to the histograms.Label the graphs as either symmetrical (mound), skewed left, skewed right, or uniform and circle where their measures of center are located.The data below shows a student’s test scores in each of their classes. Which of these classes is the student most inconsistent?Math928790100958993English70908265738095History80838590658450Science60627570749073The table below shows the area of several states.Delaware has an area of 2,000 square miles. Describe what happens to the measures of center and spread if Delaware is included in the data set.Measures of center:Measures of spread:-Mean:-Median:-IQR:-Standard Deviation:What measure of center and spread would you use to best represent the data after Delaware is included? Support your reasoning.The data table below shows the number of points scored for two basketball players during the first 14 games of the season. Player 1Player 212410101512112512516121211111517202210591511161511Fill in the 1 VAR STATS for each player_______Min_______Min_______1st Quartile _______1st Quartile_______Median _______Median_______3rd Quartile _______3rd Quartile_______Max _______Max_______IQR _______IQR_______Mean_______Mean_______Standard Deviation _______Standard Deviation_______Outliers_______OutliersConstruct a boxplot.Which player would you want on your team? Why? Justify your recommendation using mathematical reasoning (be sure to discuss measures of center and measures of spread)._________________________________________________________________________________________Additional 8th Grade Standard(s):8.SP.4 Understand that patterns of association can also be seen in bivariate categorical data by displaying frequencies and relative frequencies in a two-way table. Construct and interpret a two-way table summarizing data on two categorical variables collected from the same subjects. Use relative frequencies calculated for rows or columns to describe possible association between the two variables. For example, collect data from students in your class on whether or not they have a curfew on school nights and whether or not they have assigned chores at home. Is there evidence that those who have a curfew also tend to have chores?Ms. Kinkaid polled her students to find out which they watched most on television: reality shows, sports, or sitcoms. The results are given in the table. REALITY SHOWSPORTSSITCOMTOTALFEMALE122620MALE1017330TOTAL2219950What type of show does Ms. Kinkaid’s student watch the most?A. reality showB. sportsC. sitcomD. not enough informationWhat is the probability that a female prefers to watch a sitcom?A. 12%B. 30%C. 67%D. 6%How many males watch a reality show or sports?A. 10B. 17C. 7D. 27How many females DO NOT watch sports?A. 12B. 6C. 18D. 20What is the probability that a student is female given that she prefers sitcoms? 12%B. 67%C. 18%D. 6%Given that the student is female, what is the probability that she prefers to watch sports? 2%B. 22%D. 10%D. 4%Mr. Stamp surveyed his students as to their preference to tacos or lasagna. The Venn Diagram displays results of the 48 students.What is the probability that a student selected at random will NOT like lasagna or tacos?What is the probability that a student selected at random will like only tacos? ................
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