Probability Chapter Questions

Algebra-Geometry I DESCRIPTIVE STATISTICS

SUCCESS CRITERIA:

1) Compare and contrast the measures of Central Tendency.

2) Compare, contrast, and choose the best display for the data given.

3) Use a line of best fit to predict.

INSTRUCTION 1: KHAN ACADEMY DISRIPTIVE STATISTICS INSTRUCTION 2: SOPHIA

INSTRUCTOR: Trina Northcott Hidden Lake High School Westminster Public Schools

EMPOWER Recorded TARGET SCALE THEME

MA.09.SP.01.04 Interpret Differences in Shape, Center,& Spread of Data

MA.09.SP.02.04 Summarize Data using Frequency Tables

PMI-NJ Center for Teaching & Learning ~1~ NJCTL.org PROFICIENCY SCALE: SCORE REQUIREMENTS 4.0 In addition to exhibiting Score 3.0 performance, in-depth inferences and applications that go BEYOND what was taught in class. Score 4.0 does not equate to more work but rather a higher level of performance.

3.5 In addition to Score 3.0 performance, in-depth inferences and applications with partial success. o Determine the appropriate solution in a Real World example.

3.0 The learner exhibits no major errors or omissions regarding any of the information and processes (simple or complex) that were explicitly taught. o Compare and contrast the measures of Central Tendency, AND o Compare, contrast, and choose the best display for the data given, AND o Use a line of best fit to predict.

2.0 Can do one or more of the following skills / concepts: There are no major errors or omissions regarding the simpler details and processes as the learner… o Can calculate the mean (average), OR o Can calculate median, OR o Can calculate mode, OR o Can calculate central tendencies of real word problems, OR o Can organize date into a frequency table, OR o Can organize data into a histogram, OR o Can organize data into a stem and leaf plot, OR o Can organize data into a box and whisker plot, OR o Can use a box and whisker plot to analyze the spread of the data, OR o Can find the line of best fit using a scatter plot, OR o Can use the line of best fit to predict, OR o Can choose the best data display for a given situation.

1.0 Know and use the vocabulary  Identify the Basic Elements With help, a partial understanding of some of the simpler details and process

Measures of Central Tendency

WORD or CONCEPT DEFINITION or NOTES EXAMPLE or GRAPHIC REPRESENTATION

measures of central tendency

median

measures of spread

outliers

INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA

Classwork

1. Which of the following data sets have outlier(s)? a. 1, 5, 7, 9, 10, 11, 15 b. 25, 39, 49, 53, 56, 60 c. 18, 19, 20, 24, 30, 60 d. 70, 74, 76, 79, 82, 83

PMI-NJ Center for Teaching & Learning ~3~ NJCTL.org 2. Find the mean, median and mode of the following numbers: 4, 10, 11, 20, 21, 30, 9, 100, 21 Mean: Median: Mode:

3. Find the range: 30, 31, 28, 18, 30, 4, 1

4. Find the mean, median, mode, range, and outliers for the data below.

Candy Calories Twix 291 Reeses 232 Milky Way 228 Charleston Chew 230 Runts 60 Hershey Choc. Bar 210 Butterfinger 207 Fun Dip 150 Twizzler 160 Snickers 271 Swedish Fish 150 M&M’s 243 Skittles 231 Kit Kat 218 Baby Ruth 156

5. Find the mean, median, mode, range, and outliers for the data below.

Average Rain Fall in Atlantic City Month Inches January 3.5 February 3.1 March 3.6 April 3.6 May 3.3 June 2.6 July 3.8 August 4.1 September 2.9 October 2.8

Homework

6. Which of the following sets of data have outliers: a. 90, 92, 93, 94, 97, 100 b. 4, 20, 27, 28, 33, 34, 37 c. 64, 67, 68, 69, 73, 75, 79 d. 18, 33, 38, 39, 42, 43, 46

7. Find the mean, median, and mode for the following numbers: 5, 19, 45, 2, 4, 29, 18, 2, 7 Mean: Median: Mode:

8. Find the range: 7, 9, 17, 20, 28, 30, 31

9. Find the mean, median, mode, range, and outliers for the data below:

School Play Year Tickets Sold 1990 321 1991 370 1992 376 1993 474 1994 467 1995 474 1996 540 1997 510 1998 579 1999 603 2000 589 2001 632 2002 699 2003 730 2004 727 2005 748

10. Find the mean, median, mode, range, and outliers for the data below:

Average Temperature Trenton Month Temperature (°F) January 30° February 32° March 42° April 51° May 62° June 71° July 75° August 74° September 67° October 56°

Central Tendency Application Problems

PMI-NJ Center for Teaching & Learning ~5~ NJCTL.org Classwork

11. Your 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?

12. 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?

13. Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13

 The mean is  The mode is  The median is 15 13 14

What would happen if the value of 20 was added to the data set? How would the mean, median and mode change?

14. Consider the following data set: 13, 18, 13, 14, 13, 16, 14, 21, 13

 The mean is  The mode is  The median is 15 13 14

What 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?

15. 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.

Homework

16. Your test grades are 90, 95, 83, 89, and 91. What must you earn on the next test to receive an average of 91?

17. 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?

18. Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13

 The  The  The mean is 10.5 median is 10.5 mode is 10 and 11   What would happen if the value of 10 was added to the data set?  How would the mean median and mode change?  19. Consider the following data set: 8, 9, 10, 10, 10, 11, 11, 11, 12, 13   The  The  The mean is 10.5 median is 10.5 mode is 10 and 11   What 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 & Histograms   W OR D or  EXAMPLE or GRAPHIC  DEFINITION or NOTES CO REPRESENTATION NC EP T  fr equency table      tw o-way frequency table      hi stogram       INSTRUCTION 1: KHAN ACADEMY FREQUENCY TABLE INSTRUCTION 2: SOPHIA

 INSTRUCTION 1: KHAN ACADEMY HISTOGRAM INSTRUCTION 2: SOPHIA

PMI-NJ Center for Teaching & Learning ~7~ NJCTL.org                       

                 Classwork  21. The following are test grades from your classmates. Organize the data into a frequency table.  100 73 89  65 86 79  83 95 83  96 83 86  76 69 89  79 74 85  22. The following are times that it took children in gym class to run a mile. Organize this data into a frequency table.  7:23 8:02 10:04  7:05 7:50 9:24  6:59 9:01 8:34  7:25 8:55 6:39  7:55 11:01 9:28  8:02 9:54 8:24   23. Organize this data into a histogram.   Length of walk time Time Tally Frequency  21 35 48 10-19 III 3  63 67 11 20-29 I 1  19 31 43 30-39 IIII 4  15 44 37 40-49 IIII 4  42 34 69 50-59 0  67 60-69 IIII 4   24.

 a. How many students scored below 70? b. How many students scored a 52? c. 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 Score  92 84 76  75 85 97  67 48 87  93 87 88  79 68 66  100 99 79  88 81 80  79 99 91  Homework   26. The following is test scores from a math test. Organize these scores into a frequency table.  78 97 49  99 67 47

PMI-NJ Center for Teaching & Learning ~9~ NJCTL.org  97 84 79  87 86 51  97 89 87  84 79 75  97 84 83   27. The following is temperatures in New Jersey in August. Organize them into a frequency table  100 102 105  97 95 101  89 88 90  99 95 93  89 89 96  102 91 99  98 92 103  108 98 92   28. Organize this data into a histogram.   Length of time walked Time Tally Frequency  64 41 38 10-19 IIII 4  27 11 48 20-29 II 2  33 13 61 30-39 IIII 4  57 49 37 40-49 IIII 4  19 69 45 50-59 I 1  34 24 12 60-69 III 3    29.     A. How many students scored in the 70’s? B. How many students scored below 70? C. How many students scored 90 or above?           30. Create a histogram and a frequency table for the following data.  Test Scores   92 97 98 97 85 83 97 85 84  76 79 89 99 84 86 77 51 89  83 97 92 78 85 89      Stem-and-Leaf Plots   W OR D or  EXAMPLE or GRAPHIC  DEFINITION or NOTES CO REPRESENTATION NC EP T  st em-and-leaf plot       INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA                

PMI-NJ Center for Teaching & Learning ~11~ NJCTL.org  

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                          Classwork   31. Create a stem-and-leaf plot for the data.  Daily temperature:  80 82 79 84 86 79 92 90 96 100 97 88   32. 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 87   35. From your stem-and-leaf plot made in #34, create a histogram.       Homework   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?         

PMI-NJ Center for Teaching & Learning ~13~ NJCTL.org   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 19   40. From the stem-and-leaf plot you created in #39 create a histogram, list the mode, and list the median.     Box-and-Whisker Plots   W OR D or  EXAMPLE or GRAPHIC  DEFINITION or NOTES CO REPRESENTATION NC EP T  b ox-and-whiskers plot           lo wer quartile      u pper quartile      in ter quartile range      w hiskers      o utliers       INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA  

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             Classwork   Test Grades: 78, 82, 65, 46, 84, 99, 100, 90, 75, 59, 75, 79, 80, 86, 68   Use the data set to   41. Create a stem and leaf    42. Identify the upper and lower extremes    Find the following measures:   43. median    44. lower and upper quartiles     45. Create a box and whisker plot      

PMI-NJ Center for Teaching & Learning ~15~ NJCTL.org  Homework   Test Grades: 80, 81, 64, 66, 74, 98, 100, 91, 85, 89, 55, 66, 70, 84, 98   Use the data set to   46. Create a stem and leaf    47. Identify the upper and lower extremes    Find the following measures:   48. median    49. lower and upper quartiles     50. Create a box and whisker plot             Scatter Plots and Lines of Best Fit   W OR D or  EXAMPLE or GRAPHIC  DEFINITION or NOTES CO REPRESENTATION NC EP T  sc atter plot      li ne of best fit      pr   ediction equation     INSTRUCTION 1: KHAN ACADEMY SCATTER PLOT INSTRUCTION 2: SOPHIA

 INSTRUCTION 1: KHAN ACADEMY LINE of BEST FIT INSTRUCTION 2: SOPHIA

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        Classwork   51. Predict the test score of someone who spends 48 minutes studying. 

PMI-NJ Center for Teaching & Learning ~17~ NJCTL.org 110 105 100 95 s

e 90 r o

c 85 s

s 80 e t 75 70 65 60 25 30 35 40 45 50 55 60 Tim e spent studying     52. Predict the test score of someone who spends 34 minutes studying. 

110 105 100 95 s

e 90 r o

c 85 s

s 80 e t 75 70 65 60 25 30 35 40 45 50 55 60 Tim e spent studying    53. Draw a scatter plot from the following data:   Size of shoe Height (inches) 5 55 5.5 58 6 62 7 68  6.5 63  7.3 70  8 79  8.7 88       54. Consider the scatter graph to right   Which two points would give the line of best fit?  A and B  A and C  D and B  There is no pattern                55.Consider the scatter graph to answer the following:  Which two points would give the line of best fit?  A and B  B and C  C and D  There is no pattern

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PMI-NJ Center for Teaching & Learning ~19~ NJCTL.org              Homework   56. Using the scatter graph, predict the mile time of someone who spends 6 hours a week training.

e 9:31 m i t

M 8:19

5:55 0 5 10 15 20 25 Time spent training    57. Using the scatter graph, predict the mile time of someone who spends 12 hours a week training.

e 9:31 m i t

M 8:19

5:55 0 5 10 15 20 25 Time spent training    58. Draw a scatter graph from the following data,  Time spent studying (min) Grade 55 97 31 78 52 90 20 61 42 84 47 90 31 81   59. Consider the scatter graph to answer the following:  Which point would give the line best fit?  A  B  C  There is no pattern

  60. Consider the scatter graph to answer the following:  Which two points would give the line of best fit?  A and D  A and C  B and D  There is no pattern

PMI-NJ Center for Teaching & Learning ~21~ NJCTL.org                    Determining the Prediction Equation   Classwork   61.   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)?         10  65. Consider 9

the scatter 8 graph to answer the following: 7 The equation 6 for the line of 5 best fit is y = -1.06x + 10.7. 4 Determine the 3 value for x=15? Is this an 2 interpolation or 1 extrapolation? 0  0 1 2 3 4 5 6 7 8 9 10        

PMI-NJ Center for Teaching & Learning ~23~ NJCTL.org    Homework   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.

9 2, 9.2

8 3, 8.1

7 3.4, 7

6 4, 5.4 5

4 5.3, 4.2 7.5, 3.7 3

1 9, 1

0 0 1 2 3 4 5 6 7 8 9 10    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 Display   W OR D or  EXAMPLE or GRAPHIC  DEFINITION or NOTES CO REPRESENTATION NC EP T  d ata display       INSTRUCTION 1: KHAN ACADEMY INSTRUCTION 2: SOPHIA                         

PMI-NJ Center for Teaching & Learning ~25~ NJCTL.org                          Classwork  71. Choose the best data display to show the number of cans of soda that you drank each week for the last three months.     A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   72. 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. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   73. Chose the best data display to show the upper 50% of the scores on a Chemistry exam.   histog  A. ram B. box and whisk  circle er D. bar graph  graph  C.  F. freque E. stem- ncy and- table leaf   74. 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. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   75. Choose the best data display to show the interval of temperatures for 50% of the states.     A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf     Homework   76. 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. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   77. Choose the best data display to show the upper 25% of the scores on a History exam. 

PMI-NJ Center for Teaching & Learning ~27~ NJCTL.org    A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   78. Choose the best data display to show the number of A’s you earned each month in the past school year.     A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   79. Choose the best data display to show the interval of grades for 20% of the students.     A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf   80. Choose the best data display to show the percent of students who prefer orange juice, cranberry juice, apple juice, or soda.     A. C. E. histog freque circle ram ncy graph  table  B. box  F. and D. bar stem- whisk graph and- er leaf      Misleading Graphs   Classwork   81. 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 Preference          Homework   82. How can the makers of Crest change the graph so that the consumer thinks that far more people purchased Crest than Aquafresh?     DATA & STATISTICS UNIT REVIEW   Multiple Choice– Choose the correct answer for each question.  1. Consider the data set: 85, 84, 87, 100, 86, 75, 62   Select the measure that has the greatest value   a. Median b. Mean c. Mode d. Range 55  66  2. Consider the data set: 50, 65, 49, 100, 91, 90, 80  Select the statement that is true  a. Mode: None; Median: 100  b. Median: 80; Range: 51  c. Mean: 75; Range: 30  d. Mean: 87.5; Mode: 90.5   3. 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. 78  

PMI-NJ Center for Teaching & Learning ~29~ NJCTL.org  4. 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 minutes     5. Use the histogram to determine the number of students that scored below a 70.  a. 8 b. 10 c. 25. d. 17

            6. Use the stem-and-leaf plot to find the median  a. 89 b. 80.9 c. 84 d. 94          Key: 4 2 = 42  7. Use the box and whisker plot to determine the true statement.    50% of the data is:  a. between 105 and 132

b. between 87 and 122

c. between 122 and 147

d. between 87 and 132    8. Use the box and whisker plot to determine the range    a. 60 b. 87 c. 123 d. 150     Using the scatter graph below answer questions #9 and #10  9. Predict the mile time of someone who spent 8 hours training.  a. 9:23 b. 6:09 c. 7:40 d. 8:37   10. 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 training  d.There is no correlation between the time spent training and the time it takes to run a  mile

    11. Given the points (2, 6) and (8, 12) on a scatter graph, determine the equation for the best line of fit.  a. y=-6x+4 b. y= x+4 c. y=4x+6 d. y= x - 4     

PMI-NJ Center for Teaching & Learning ~31~ NJCTL.org  12. 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.  a. 50.48 b. 78.8 c. 91.7 d. 98   13. Choose the best data display to show the time you spend on various activities throughout the day.  A. histogram  B. box and whisker  C. frequency table  D. bar graph  E. circle graph  F. stem-and-leaf      Short Constructed Response – Write the correct answer for each question. No partial credit will be given. 14. 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    15. What score must Fred obtain on his 6th test to have an 81 average?

  Test Grades: 89, 78, 85, 71, 88             16. Find the median, given the stem and leaf                     17. A 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.  18. Use the data in the table to create the following:    85 79 68    80 89 79    7 80 68 0  

PMI-NJ Center for Teaching & Learning ~33~ NJCTL.org