Unit 2- Patterns in Data 9 Days NAME

Unit 2- Patterns in Data 9 days NAME:

Objectives / Yes- I do understand / No- I do not understand. I need more help / Explanation.
Exploring Distribution
Construct dot plots, histograms, and relative frequency histograms
Describe the shape of a distribution
Compute and interpret the mean, median and mode (from a list of values and form a frequency table)
Estimate the mean and median from a histogram
Use the relationship between the mean, total, and the number of values to find a missing value given the mean and the other values
Objectives / Yes- I do understand / No- I do not understand. I need more help / Explanation.
Variability
Find and interpret percentiles and quartiles as measures of the position of a value in a distribution
Find the five-number summary and the interquartile range (IQR)and interpret the IQR as a measure of variability
Determine if a value is an outlier
Construct and interpret a box plot
Compute and interpret deviations from the mean
Compute or estimate and interpret the standard deviation as a measure of spread
Predict 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 number

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.

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.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 Tendency

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

Find the mean, median and mode of the following numbers:

4, 10, 11, 20, 21, 30, 9, 100, 21

Mean:

Median:

Mode:

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

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

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

Average Rain Fall in Atlantic City

MonthInches

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

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

Find the mean, median, and mode for the following numbers:

5, 19, 45, 2, 4, 29, 18, 2, 7

Mean:

Median:

Mode:

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

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

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

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?

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, 13

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

What 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, 13

The mean is 15
The mode is 13
The median is 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?

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, 13

The mean is 10.5
The median is 10.5
The 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?

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

The mean is 10.5
The median is 10.5
The 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

The following are test grades from your classmates. Organize the data into a frequency table.

1007389

658679

839583

968386

766989

797485

The following are times that it took children in gym class to run a mile. Organize this data into a frequency table.

7:238:0210:04

7:057:509:24

6:599:018:34

7:258:556:39

7:5511:019:28

8:029:548:24

23. Organize this data into a histogram.

Length of walk time

213548

636711

193143

154437

423469

Time Tally Frequency

10-19 III3

20-29 I1

30-39 IIII4

40-49 IIII4

50-59 0

60-69 IIII4

24.

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 Score

928476

758597

674887

938788

796866

1009979

888180

799991

26. The following is test scores from a math test. Organize these scores into a frequency table.

789749

996747

978479

878651

978987

847975

978483

27. The following is temperatures in New Jersey in August. Organize them into a frequency table

100102105

9795101

898890

999593

898996

1029199

9892103

1089892

Organize this data into a histogram.

Length of time walked

644138

271148

331361

574937

196945

342412

Time Tally Frequency

10-19 IIII4

20-29 II2

30-39 IIII4

40-49 IIII4

50-59 I1

60-69 III3

29.

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 Scores

929798

978583

978584

767989

998486

775189

839792

788589

Stem-and-Leaf Plots

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.

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 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

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

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

51. 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)

555

5.558

662

768

6.5 63

7.3 70

8 79

8.7 88

54. Consider the scatter graph to answer the following:

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

56. 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)Grade

5597

3178

5290

2061

4284

4790

3181

59. Consider the scatter graph to answer the following:

Which point would give the line best fit?

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

Determining the Prediction Equation

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)?

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 Display

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. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-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. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

73. Chose the best data display to show the upper 50% of the scores on a Chemistry exam.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-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. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

75. Choose the best data display to show the interval of temperatures for 50% of the states.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

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. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

77. Choose the best data display to show the upper 25% of the scores on a History exam.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

78. Choose the best data display to show the number of A’s you earned each month in the past school year.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

79. Choose the best data display to show the interval of grades for 20% of the students.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

80. Choose the best data display to show the percent of students who prefer orange juice, cranberry juice, apple juice, or soda.

A. histogram

B. box and whisker

C. frequency table

D. bar graph

E. circle graph

F. stem-and-leaf

Misleading Graphs

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

82. How can the makers of Crest change the graph so that the consumer thinks that far more people purchased Crest than Aquafresh?

Unit Review

Multiple 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 value

a. Median b. Mean c. Mode d. Range

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

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.

8 b. 10 c. 25. d. 17

6. Use the stem-and-leaf plot to find the median

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:

between 105 and 132
between 87 and 122
between 122 and 147
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. 9:23b. 6:09c. 7:40d. 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+4b. y= x+4c. y=4x+6d. y= x - 4

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.

50.48b. 78.8c. 91.7d. 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.

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

Find the median, given the stem and leaf

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.