Unit 2- Patterns in Data 9 days NAME:



ObjectivesYes- I do understandNo- I do not understand. I need more helpExplanation.Exploring DistributionConstruct dot plots, histograms, and relative frequency histogramsDescribe the shape of a distributionCompute and interpret the mean, median and mode (from a list of values and form a frequency table)Estimate the mean and median from a histogramUse the relationship between the mean, total, and the number of values to find a missing value given the mean and the other valuesObjectivesYes- I do understandNo- I do not understand. I need more helpExplanation.Variability Find and interpret percentiles and quartiles as measures of the position of a value in a distributionFind the five-number summary and the interquartile range (IQR)and interpret the IQR as a measure of variabilityDetermine if a value is an outlierConstruct and interpret a box plotCompute and interpret deviations from the meanCompute or estimate and interpret the standard deviation as a measure of spreadPredict the effect on the shape, center, and spread of a distribution when same number is added to each value or when each value is multiplied by the same numberCurriculum Standards:Summarize, represent, and interpret data on a single count or measurement variable.S.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).S.ID.A.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 sets.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).S.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.Essential Questions:What are the different methods of data representation and what kinds of data do we use to create them?How can given data representations be interpreted?What are the advantages and disadvantages of each method of data representation?How can data be misrepresented?How can we use summary statistics and data representations to describe a distribution or support or refute a claim?How can understanding statistics and their appropriate use be important and useful to us?Curriculum Standards:Summarize, represent, and interpret data on a single count or measurement variable.S.ID.A.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).S.ID.A.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 sets.S.ID.A.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).S.ID.B.5 Summarize categorical data for two categories in two-way frequency tables. Interpret relative frequencies in the context of the data (including joint, marginal, and conditional relative frequencies). Recognize possible associations and trends in the data.S-ID.6** Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.S-ID.7** Interpret the slope (rate of change) and the intercept (constant term) of a linear model in context of the data.S-ID.8** Compute (using technology) and interpret the correlation coefficient of a linear fit.S-ID 9 **Distinguish between correlation and causation. Measures of Central TendencyWhich of the following data sets have outlier(s)?1, 5, 7, 9, 10, 11, 1525, 39, 49, 53, 56, 6018, 19, 20, 24, 30, 6070, 74, 76, 79, 82, 83Find the mean, median and mode of the following numbers:4, 10, 11, 20, 21, 30, 9, 100, 21Mean:Median:Mode:Find the range: 30, 31, 28, 18, 30, 4, 1Find the mean, median, mode, range, and outliers for the data below. Candy CaloriesTwix291Reeses232Milky Way228Charleston Chew230Runts60Hershey Choc. Bar210Butterfinger207Fun Dip150Twizzler160Snickers271Swedish Fish150M&M’s243Skittles231Kit Kat218Baby Ruth156Find the mean, median, mode, range, and outliers for the data below. Average Rain Fall in Atlantic City MonthInchesJanuary3.5February3.1March3.6April3.6May3.3June2.6July3.8August4.1September2.9October2.8Which of the following sets of data have outliers:90, 92, 93, 94, 97, 1004, 20, 27, 28, 33, 34, 3764, 67, 68, 69, 73, 75, 7918, 33, 38, 39, 42, 43, 46Find the mean, median, and mode for the following numbers:5, 19, 45, 2, 4, 29, 18, 2, 7Mean:Median:Mode:Find the range: 7, 9, 17, 20, 28, 30, 31Find the mean, median, mode, range, and outliers for the data below: School Play Year Tickets Sold1990321199137019923761993474199446719954741996540199751019985791999603200058920016322002699200373020047272005748Find the mean, median, mode, range, and outliers for the data below: Average Temperature Trenton Month Temperature (°F)January30°February32°March42°April51°May62°June71°July75°August74°September67°October56° Central Tendency Application ProblemsYour test grades are 70, 85, 95, 93, and 94. You have one more test and want an average of an 86. What must you earn on your next test?Your test grades are 60, 55, 68, 78, 80, 68, and 72. To pass this class your average must be a 70 or above. You have one more test to take. Is it possible for you to pass this class? Why or why not? If you can pass the class what score must you earn on the next test?Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13The mean is 15The mode is 13The median is 14What would happen if the value of 20 was added to the data set?How would the mean, median and mode change?Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13The mean is 15The mode is 13The median is 14What would happen if a value “x”, was added to the set?How would the median change:If x was 16?If x was another number in the list other than 16?If x was a number not on the list?Consider the data set: 70, 74, 77, 80, and 83. Identity the data values that remain the same if the value “x”, which is less than 70, is added to the set of data.Your test grades are 90, 95, 83, 89, and 91. What must you earn on the next test to receive an average of 91?You are comparing grades with a friend and he tells you that you cannot earn an A in the class. To receive an A in the class your test average must be a 93 or above. Your grades are 100, 79, 80, 92, 87, 60, and a 93. You still have one more test left. Is it possible to get an A in this class? Why or why not? If it is possible to earn an A what must you get on your next test?Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13The mean is 10.5The median is 10.5The mode is 10 and 11What would happen if the value of 10 was added to the data set?How would the mean median and mode change?Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13The mean is 10.5The median is 10.5The mode is 10 and 11What would happen if a value of “x” was added to the set?How would the mean change?If x was not 12?If x was another number on the list other than 12?If x was a number not on the list?20. Consider the data set: 48, 52, 55, 58, 60. Identify the data values that remain the same if “x”, a number greater than 55, is added to the data set. Frequency Tables & HistogramsThe following are test grades from your classmates. Organize the data into a frequency table.1007389658679839583968386766989797485The following are times that it took children in gym class to run a mile. Organize this data into a frequency table.7:238:0210:047:057:509:246:599:018:347:258:556:397:5511:019:288:029:548:2423. Organize this data into a histogram.Length of walk time21354863671119314315443742346967Time Tally Frequency10-19 III320-29 I130-39 IIII440-49 IIII450-59 060-69 IIII424.How many students scored below 70?How many students scored a 52?Can you determine the exact value of the test grade that was in the 60’s?25. Create a frequency table and a histogram for the data below. Tests Score928476758597674887938788796866100997988818079999126. The following is test scores from a math test. Organize these scores into a frequency table.78974999674797847987865197898784797597848327. The following is temperatures in New Jersey in August. Organize them into a frequency table1001021059795101898890999593898996102919998921031089892Organize this data into a histogram.Length of time walked644138271148331361574937196945342412Time Tally Frequency10-19 IIII420-29 II230-39 IIII440-49 IIII450-59 I160-69 III329.How many students scored in the 70’s?How many students scored below 70?How many students scored 90 or above?30. Create a histogram and a frequency table for the following data. Test Scores929798978583978584767989998486775189839792788589 Stem-and-Leaf Plots31. Create a stem-and-leaf plot for the data.Daily temperature:80 82 79 84 86 79 92 90 96 100 97 8832. What is the median of the data of the following stem-and-leaf plot?33. What is the mode of the data in the following stem-and-leaf plot?34. Make a stem-and-leaf plot from the following data.Test scores:87 88 89 79 57 69 68 99 91 85 89 75 89 94 92 91 84 8735. From your stem-and-leaf plot made in #34, create a histogram.36. Create a stem-and-leaf plot for the data:Test scores:67 89 84 95 91 97 69 76 81 73 94 74 86 81 92 76 54 60 37. What is the median of the data in the following stem-and-leaf plot?38. What is the mode of the data in the following stem-and-leaf plot?39. Make a stem-and-leaf plot from the following data.Time spent walking:20 24 10 8 32 27 28 10 15 34 9 34 35 25 31 27 28 1940. From the stem-and-leaf plot you created in #39 create a histogram, list the mode, and list the median.Box-and-Whisker PlotsTest Grades: 78, 82, 65, 46, 84, 99, 100, 90, 75, 59, 75, 79, 80, 86, 68Use the data set to 41. Create a stem and leaf42. Identify the upper and lower extremesFind the following measures:43. median44. lower and upper quartiles45. Create a box and whisker plotTest Grades: 80, 81, 64, 66, 74, 98, 100, 91, 85, 89, 55, 66, 70, 84, 98Use the data set to 46. Create a stem and leaf47. Identify the upper and lower extremesFind the following measures:48. median49. lower and upper quartiles50. Create a box and whisker plot Scatter Plots and Lines of Best Fit51. Predict the test score of someone who spends 48 minutes studying.52. Predict the test score of someone who spends 34 minutes studying.53. Draw a scatter plot from the following data:Size of shoeHeight (inches)55586268 6.5 63 7.3 70 8 79 8.7 8854. Consider the scatter graph to answer the following:Which two points would give the line of best fit?A and BA and CD and BThere is no pattern55.Consider the scatter graph to answer the following:Which two points would give the line of best fit?A and BB and CC and DThere is no pattern56. Using the scatter graph, predict the mile time of someone who spends 6 hours a week training.57. Using the scatter graph, predict the mile time of someone who spends 12 hours a week training.58. Draw a scatter graph from the following data,Time spent studying (min)Grade9778906184908159. Consider the scatter graph to answer the following: Which point would give the line best fit?ABCThere is no pattern60. Consider the scatter graph to answer the following:Which two points would give the line of best fit?A and DA and CB and DThere is no pattern Determining the Prediction Equation61. Use the two points (7,14) and (15,27) to write an equation for the line of best fit.62. If the prediction equation is y=.5t+60, where t represents time in minutes, what will the person get on his test if he studies for 45 minutes?63. If the prediction equation to determine a test grade is y=.5t+60, and someone received an 80 on the test, how long did they study for?64. Consider the scatter graph to answer the following: What is the slope of the line of best fit that passes through (3.4, 7) and (8, 3)?What is the y-intercept of the line of best fit that passes through (3.4, 7) and (8, 3)?65. Consider the scatter graph to answer the following: The equation for the line of best fit is y = -1.06x + 10.7. Determine the value for x=15? Is this an interpolation or extrapolation?66. Using the scatter graph below use the two points (3.4, 7) and (9, 1) to write an equation for the line of best fit.67. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, what grade will someone earn if they study for 30 minutes.68. If the prediction equation for a test grade is y=.52t+65, where t represents the time in minutes, how long did someone study for if they received an 83 on the exam?69. Consider the scatter graph to answer the following: What is the slope of the line of best fit passing through (2.7, 11.1) and (9.4, 3.7)?What is the y-intercept of the line of best fit passing through (2.7, 11.1) and (9.4, 3.7)?70. Consider the scatter graph below. The equation for the line of best fit is y= -.98x+13.6. Determine the value for x=5.Is this an interpolation or extrapolation? Choosing A Data Display71. Choose the best data display to show the number of cans of soda that you drank each week for the last three months.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf72. Chose the best data display to show the number of students that earned an A, B, C, D, F on their English final exam.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf73. Chose the best data display to show the upper 50% of the scores on a Chemistry exam.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf74. Chose the best data display to show the percent of students that earned an A, B, C, D, & F on their Earth’s Fury final exam.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf75. Choose the best data display to show the interval of temperatures for 50% of the states.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf76. Choose the best data display to show the percent of students that earned a gold, silver, and bronze medal at the battle of classes.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf77. Choose the best data display to show the upper 25% of the scores on a History exam.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf78. Choose the best data display to show the number of A’s you earned each month in the past school year.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf79. Choose the best data display to show the interval of grades for 20% of the students.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leaf80. Choose the best data display to show the percent of students who prefer orange juice, cranberry juice, apple juice, or soda.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leafMisleading Graphs81. If you owned stock in M&M’s candy, which graph would you want placed on a billboard?Percentage of Mrs. Smith’s Students’ Candy Preference82. How can the makers of Crest change the graph so that the consumer thinks that far more people purchased Crest than Aquafresh?Unit ReviewMultiple Choice– Choose the correct answer for each question. Consider the data set: 85, 84, 87, 100, 86, 75, 62 Select the measure that has the greatest valuea. Median b. Mean c. Mode d. Range2. Consider the data set: 50, 65, 49, 100, 91, 90, 80 Select the statement that is truea. Mode: None; Median: 100b. Median: 80; Range: 51c. Mean: 75; Range: 30d. Mean: 87.5; Mode: 90.53. Mark has the following test grades: 85, 98, 79, 82, 100, 83 What must Mark score on the one remaining test, if he wants his test average to be an 86? a. 86 b. 75 c. 74 d. 783286125317504. Use the frequency table to determine the number of people that ran the race in one hour or more. a. 3 b. 0 c. 16 d. 13 Race time in minutes3912870-4711705. Use the histogram to determine the number of students that scored below a 70. 8 b. 10 c. 25. d. 172788920-2743206. Use the stem-and-leaf plot to find the median 89 b. 80.9 c. 84 d. 94Key: 4 2 = 427. Use the box and whisker plot to determine the true statement.2276475444550% of the data is:between 105 and 132between 87 and 122between 122 and 1472790825259715between 87 and 1328. Use the box and whisker plot to determine the rangea. 60 b. 87 c. 123 d. 150Using the scatter graph below answer questions #9 and #109. Predict the mile time of someone who spent 8 hours training.a. 9:23b. 6:09c. 7:40d. 8:3710. Which of the following statements reflect the data on the scatter graph?a. The less time spent training, the greater the mile time b. The more time spent training, the lower the mile time c. The points on the graph indicate that one can predict the mile time, given the time spent trainingd.There is no correlation between the time spent training and the time it takes to run a mile11. Given the points (2, 6) and (8, 12) on a scatter graph, determine the equation for the best line of fit.a. y=-6x+4b. y= x+4c. y=4x+6d. y= x - 412. If the prediction equation for a student’s test grade is y=.48t+ 50, where t is the time spent studying in minutes. Calculate the grade of someone who studied for one hour.50.48b. 78.8c. 91.7d. 9813. Choose the best data display to show the time you spend on various activities throughout the day.A. histogramB. box and whiskerC. frequency tableD. bar graphE. circle graphF. stem-and-leafShort Constructed Response – Write the correct answer for each question. No partial credit ?will be given. What measure of central tendency is the largest for the given set of data and what is its value? 58, 62, 80, 83, 71, 69, 95, 96, 71 What score must Fred obtain on his 6th test to have an 81 average?Test Grades: 89, 78, 85, 71, 88 31051503810Find the median, given the stem and leafA line of best fit has been drawn on the graph below, insert points on the graph that would make this the appropriate line of best fit.Extended Constructed Response – Solve the problem, showing all work. Partial credit may be given.Stem-and-leaf plotBox and whisker plotWhat information can be found from a stem and leaf plot? d. What information can be found from a box and whisker graph?18. Use the data in the table to create the following: 857968808979708068Answer Key1. b,cmean= 25.1median= 20 mode= 213. range= 30mean= 202.47median= 218mode= 150 range= 231outliers= 605. mean= 3.33median= 3.4mode= 3.6 range= 1.5 outliers= none6. b,d7. mean= 12.6median= 7mode= 2 range= 249. mean= 552.44median= 559.5mode= 474range= 427outliers= none10. mean= 56median= 59mode= no mode range= 45 outliers= none 79yes because you can get a 79 or above.The mean would change by .5, the mode and median would not change. x=16: median would be still be 14 (wouldn’t change). x was another # on list: median would still be 14 unless x<14. x was another # not on list: median would still be 14 unless x<14. mode and maximum98not possible. The mean would not change, the median would change by .5 to 10, and the mode would change to just 10. x not = 12: mean would decrease if #<12 and increase if #>12. x was another # on list: mean would decrease if #<12 and increase if #>12.x was another # not on list: mean would decrease if #<12 and increase if #>12.mode and minimum Grade Tally Frequency 60-66I167-73II274-80III381-87IIIII I688-94II295-101III322. Time TallyFrequency 6:30-7:10 III37:11- 7:51III37:52- 8:32IIII48:33-9:13III39:13 - 9:53II29:54- 10:34II210:35-11:15I123.12192006365875a. 2 b. 0 8509003749675c. No 25. Test ScoresTally Frequency 45-54I155-64065-74III375-84IIIII III885-94IIIII III895-104 IIII426. Test ScoresTally Frequency 45-54III355-64065-74I175-84IIIII III885-94IIII495-104IIIII 52102870060864757.TemperatureTallyFrequency 85-88I189-92IIIII II793-96IIII497-100IIIII I6101-104IIII4105-108II228.a. 4 b. 3 c. 230. Test ScoresTallyFrequency 50-58I159-67068-76I177-85IIIII IIIII1086-94IIIII I695-102IIIII I6385090037623751.79982468926710032. median=8 mode= none 34.576897598457789999112491048385223075535. 36. 5460 797346681146991245737. median= 68 38. mode= 48,68,89 39. 08910 0 59245778831244540.mode= 10,27,28,34, median= 27465965875589824690 91001109345245046541. 42. upper extreme= 100 ; lower extreme= 4643. median= 78.544. lower quartile= 62.25 ; upper quartile= 89.25 45. 4662.2578.589.2510046. 5564667481459918810047. upper extreme= 100 ; lower extreme=5548. median= 8449. lower quartile= 69.5 ; upper 8763006480175quartile= 9250. 5569.5849210051. 90 7553. 54. A and C 1499235224282055. There is no pattern56. 8:03 7:0758. 59. B60. B and D 61. y = (13/8)x + 21/8 62. 82.563. 40 minutes64. slope= -4/4.6; y-intercept= 45.8/4.665. y= -5.2; extrapolation 66. y= (-6/5.6)x + 59.6/5.6 67. 80.668. 34.6 minutes 69. slope= -7.4/6.7; y-intercept= 94.35/6.7 70. y=8.7; interpolation71. A72. D73. B74. E75. C76. E77. B78. A79. C80. E81. 2nd Graph (bottom graph) change the scaleChapter Review abbabcbaca&bbba14. mean75median=144.5 points will varya. 68870 99800 59b. 6873.5798489mean, median, mode, range, lower extrema, upper extremad. median, range, lower extrema, upper extrema, upper quartile, lower quartile ................
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