Algebra. Chapter 10: Data Analysis. Name: Teacher: Pd:

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1 Algebra Chapter 10: Data Analysis Name: Teacher: Pd:

2 Table of Contents o (Day 1): SWBAT: Displaying Data using Frequency Histograms Pgs: #1 10 HW: Pgs o (Day 2): SWBAT: Measures of Central Tendency Pgs: #16 21 HW: Pgs o (Day 3): SWBAT: Box and Whisker Plots Pgs: #26-31 HW: Pgs o (Day 4): SWBAT: Univariate/Bivariate Data Pgs: #36-45 HW: Pgs o (Day 5): SWBAT: Equations of Best Fit Lines Pgs: #50-54 HW: Pgs 55-56

3 Day 1 Displaying Data using Frequency Histograms Warm Up Quantitative vs. Qualitative Qualitative Quantitative Deals with descriptions Deals with numbers Data can be observed but not measured Data which can be measured Colors, textures, smells, tastes, appearance, Length, height, area, volume, weight, speed, Example 1: Differentiating Between Qualitative Data and Quantitative time, temperature, Data cost, members, ages, etc. beauty etc. Quantitative Quantity Qualitative Quality Regents Practice

4 Causal Relationship - Correlation. Causation is when a change in one quantity causes a change in a second quantity. For example, as study time increases, test scores increase. 3) Sources of Bias in a Survey 2

5 Biased vs. Unbiased Biased Influence in an unfair way; inclination towards something; predisposition, partiality, prejudice, preference Studying only one group all girls, all people in their 20s, all people who weigh 150 lbs. Unbiased Studying a variety of groups boys and girls, old and young, thin and fat, short and tall 4) 5) 3

6 The of a data value is the number of times it occurs. A shows the frequency of each data value. If the data is divided into intervals, the table shows the frequency of each interval. Enrollment in Western Civilization Classes Example 6 : 4

7 A is a bar graph used to display the frequency of data divided into equal intervals. The bars must be of equal width and should touch, but not overlap. 7) 5

8 Constructing Histograms 8) The Jacksonville High School Varsity Boys basketball team had an excellent season, compiling a record of 15 5 (15 wins and 5 losses). The total points scored by the team for each of the 20 games are listed below in the order in which the games were played: 76, 55, 76, 64, 46, 91, 65, 46, 45, 53, 56, 53, 57, 67, 62, 64, 67, 52, 58, 62 (a) Complete the frequency table below. Explain your answers here! (b) On the graph grid provided, create a histogram using the frequency table from above. c) What percentage of the points are between 80-89? 6

9 Cumulative Frequency Histograms shows the frequency of all data values less than or equal to a given value. You could just count the number of values, but if the data set has many values, you might lose track. Recording the data in a cumulative frequency table can help you keep track of the data values as you count. Example 9: 7

10 Example 10: Twenty students were surveyed about the number of days they played outside in one week. The results of this survey are shown below. {6, 5, 4, 5, 0, 7, 1, 5, 4, 4, 3, 2, 2, 3, 2, 4, 3, 4, 0, 7} Complete the frequency table for these data Number of Days Outside Interval Tally Frequency Complete the cumulative frequency table using these data. Number of Days Outside Cumulative Interval Frequency What must the last entry of the cumulative frequency table always be equal to? Explain. Create a cumulative frequency histogram based on the table you made. 8

11 Example 11: The Cumulative Frequency Histogram below shows test scores from an Algebra Regents Exam. a) Determine the total number of students who took the Algebra Regents Exam. b) Determine how many students scored higher than 70. c) State which ten-point interval contains the median. d) State which ten-point interval doubled another ten-point interval. 9

12 SUMMARY Exit Ticket 10

13 Day 1 - HW 11

14 12

15 14) 15) 13

16 16) 14

17 17) 15

18 Day 2 - Measures of Central Tendency SWBAT: Calculate the Measures of Central Tendencies Warm Up 1. Questions 2 4 refer to the following: 16

19 Example 1: Example 2: 17

20 In Summary: *If your data set contains an outlier, use the to represent the data. * If your data set does not contain an outlier, use the to represent the data. Example 3: Practice a) Fdf b) Mean = Median = Mode = 18

21 What will happen to the measures of central tendency if we add the same amount to all data values, or multiply each data value by the same amount? Example 4: Given the following list of students' scores on a quiz: 10, 24, 14, 30, 40, 28, 14 Part a: Determine the median of these scores. Determine the mode of these scores. Part b: The teacher decides to adjust these scores by adding four points to each score. Explain the effect, if any, that this will have on the median and mode of these scores. 19

22 Missing Value Problems and Mean. Example 5: Example 6: Practice : 20

23 21

24 Day 2 HW

25

26

27

28 Day 3 Box and Whisker Plots Warm - Up 1. Gfgf 2. Quartiles can be thought of as percentile measure. Remember that quartiles break the data set into 4 equal parts. If 100% is broken into four equal parts, we have subdivisions at 25%, 50%, and 75% creating the: First quartile (lower quartile) to be at the 25 th percentile. Median (or second quartile) to be at the 50 th percentile. Third quartile (upper quartile) to be a the 75 th percentile. 5-Statistical Summary Minimum: the smallest value in the set 1 st Quartile: the middle value in the first half of the set 2 nd Quartile: the middle value 3 rd Quartile: the middle value in the second half of the set Maximum: the largest value in the set Box and Whisker Plot 26

29 Using Quartiles to Answer Data Questions Part b: Part c: Part d: 27

30 Box and Whisker Plot Practice Problems Example 3: Part a: Example 4: Explain your answers here! Example 5: Explain your answers here! 28

31 Example 6: Explain your answers here! Example 7: 29

32 Example 8: The average length in inches of the ten longest bones in the human body are listed. Use a graphing calculator to make a box-and-whisker plot to display the data 58, 63, 40, 44, 57, 59, 61, 53, 54, 58, 57, 57, 58, 58, 56 Example 9: Shown below are the scores 16 students received on a math quiz. Label the Minimum, Q1, Q2, Q3, and Maximum. 5-Statistic Summary: Minimum: 1 st quartile: 2 nd quartile (median): 3 rd quartile: Maximum: 52, 60, 66, 66, 68, 72, 72, 73, 74, 75, 80, 82, 84, 91, 92, 98 30

33 SUMMARY Exit Ticket 31

34 Day 3 HW

35 3. 4. Twenty of Mr. Greco s physics students recently took a quiz. The results of this quiz are shown in the following box-and-whiskers diagram. Assume that all scores are whole numbers. Ex pla (a) What is the median score of the math quizzes? (b) What is the range of the scores on the math quizzes? (c) Mr. Greco regularly sets the passing grade on his quizzes to be the score of the lower quartile. What is the passing grade on this quiz? (d) What is the highest score on Mr. Greco s quiz? 33

36

37 8. 9) 35

38 (Day 4) Univariate/Bivariate Data SWBAT: Determine whether the data to be analyzed is univariate or bivariate Create a scatter plot of bivariate data Warm Up

39 The Scatterplot So far, in this unit, we have been collecting data that represents only one concept or variable. Such data is described as univariate data and is normally represented in a frequency table or histogram. Examples of Univariate Data Value of Houses in a Neighborhood Variable = In this lesson, we will explore examples of bivariate data. data compares quantities and determines if there is a relationship between them. Bivariate data is often represented with a scatterplot. Look at the examples below. 37

40 1) 2) Correlation A correlation describes a relationship between two data sets. A graph may show the correlation between data. The correlation can help you analyze trends and make predictions. There are three types of correlations between data. 38

41 Scatter Plots and the Line of Best Fit When you graph a scatter plot, it is helpful to know the general behavior of the data. Is it going up, down, or nowhere? It is also helpful to make predictions if the behavior of the data continues in the same direction. To do this, we can draw a straight line on the graph, called the line of best fit, or trend line. This line helps show the correlation between data sets more clearly. It can also be helpful when making predictions based on the data. Scatterplot without line of best fit Scatterplot with line of best fit 39

42 Example 4: 1) 5) 40

43 You try It! Questions 6 and 7 refer to the diagram below. 6) hjfhjh 7) 41

44 Creating a Line of best Fit 8) 42

45 9) 43

46 SUMMARY 44

47 Exit Ticket 45

48 Day 4 - HW Identify each data set as univariate or bivariate. 1) The number of candy bars each person in a chemistry class can eat 2) Number of hours studying vs. number of hours on the phone 3) Hours spent in sunlight vs. the height of a plant 4) 5) 6) 7) 46

49 8) 9) 10) 11) 12) 47

50 13) Part a: Using the best fit line, predict the profit for 16 months. Part b: Using the best fit line, predict whether Megan and Bryce will reach their goal in the 18 th month of their business. 48

51 14) 49

52 Day 5: Equations for Lines of Best Fit Warm Up: 50

53 Example 1: You Try it! The scatter plot is graphed for you below. Draw a best fit line and predict the y-value when x =

54 Lines of best fit can be used to determine whether slopes for two sets of data are approximately equal, indicating a similarity in the relationships. 80 The equation of the line of best fit will be in the form: y = mx + b or A trend line (Best Fit Line) is not precise. Thus, your lines and equations may differ from other s slightly. (b) Write an equation for the line of best fit. Round your answers to the nearest tenth. Step 1: Choose 2 points that are on your best fit line. (, ) and (, ) Step 2: Step 3: 52

55 You Try it! (b) Write an equation for the line of best fit. Round your answers to the nearest tenth. (b) Use your answer from above to determine the number of applicants in the year

56 SUMMARY Example 2: Exit Ticket 54

57 Day 5 HW 1) The table shows the percent of people ages who report they voted in the presidential elections. Graph a scatter plot using the given data. b) Write an equation for the line of best fit. c) Use your answer from above to predict the percent of people who voted in

58 2) The table shows the number of soft drinks sold as a small restaurant from 11:00 am to 1:00 pm. (a) Graph a scatter plot using the given data. b) Write an equation for the line of best fit. c) Use your answer from above to predict the number of drink at 5:00. 56

59 Data and Statistics Review Day 6 Find the mean, median, mode, and range for the following sets of data listed below. 1) 13, 14, 15 2) 5, 6, 7, 7, 8, 9 Mean: Median: Mean: Median: Mode: Range: Mode: Range: 3) 20, 20, 20, 20 4) 15, 6, 2, 8, 5, 10, 16, 12 Mean: Median: Mean: Median: Mode: Range: Mode: Range: 5) Rosario and Enrique are in the same mathematics class. On the first five tests, Rosario received scores of 78, 77, 64, 86, and 70. Enrique received scores of 90, 61, 79, 73, and 87. How much higher was Enrique s average than Rosario s average? 6) From January 3 to January 7, Buffalo recorded the following daily high temperatures: 5, 7, 6, 5, and 7. Which statement about the temperatures is true? (a) 15 points (b) 2 points (c) 3 points (d) 4 points (a) mean = median (b) mean = mode (c) median = mode (d) mean median 57

60 The accompanying box-and-whisker plot represents the scores earned on a science test. 7) According to the diagram shown, what is the median score? (a) 75 (c) 85 (b) 70 (d) 77 8) According to the diagram shown, what score represents the first quartile? (a) 55 (c) 100 (b) 70 (d) 75 9) What statement is not true about the box and whisker plot shown? (a) 75 represents the mean score (b) 100 represents the maximum score (c) 85 represents the 3rd quartile (d) 55 represents the minimum score 10) A score of an 85 on the box-and-whisker plot shown refers to (a) the third quartile (b) the maximum score (c) the median (d) the mean The number of text messages 10 different students sent in 1 day is shown in the box-and-whisker plot below. 11) What is the minimum number of text messages sent according to the plot shown? (a) 0 (c) 2 (b) 20 (d) 8 12) What number is at the 50th percentile according to the plot shown? (a) 12 (c) 8 (b) 14 (d) 10 13) According to the plot shown, between what two numbers does half of the data lie? (a) 10 and 12 (c) 8 and 12 (b) 8 and 14 (d) 2 and 20 14) According to the plot shown, how many text messages are at the 75th percentile (upper quartile)? (a) 15 (c) 12 (b) 13.5 (d) 14 58

61 59

62 In order to pass a driver's safety course, a person must answer at least 45 out 50 questions correctly. The cumulative histogram below gives the scores of a group of people who passed the exam. 15) According to the table shown, how many total people passed the driver's safety exam? (a) 25 (c) 57 (b) 50 (d) 20 16) According to the table shown, how many people received a score of 48 or less? (a) 23 (c) 9 (b) 11 (d) 25 17) According to the table shown, how many people answered 49 questions correctly? (a) 5 (c) 9 (b) 14 (d) 41 18) The accompanying histogram shows the heights of the students in Kyra's health class. 19) The accompanying histogram shows the height distribution for students in a high school mathematics class. What is the total number of students in the class? (a) 15 (c) 209 (b) 16 (d) 5 20) Using the cumulative frequency table, how many students received a test score between a 70-79? What is the total number of students in the class? (a) 28 (c) 26 (b) 49 (d) 11 21) The test scores for 10 students in Ms. Sampson's homeroom were 61, 67, 81, 83, 87, 88, 89, 90, 98, and 100. Which frequency table is accurate for this set of data? (a) 0 (c) 80 (b) 12 (d) 26 (a) (c) (b) (d) 60

63 22) The number of calls from motorists per day for roadside service was recorded for the month of December The results were as follows: Set up a frequency table for this set of data values. Interval Tally Frequency Fill in the cumulative frequency table and create a cumulative histogram for this set of data values. Interval Cumulative Frequency 61

64 Day 7 - Chapter 10A Review Data Analysis SWBAT: Apply Their Knowledge on Data Analysis 1. According to the box-and-whisker plot shown below, what is the third quartile value? [A] 70 [B] 80 [C] 90 [D] Data regarding the students in the senior class: 578 students, 236 honor students, 150 scholarship winners, 51% male. This data can be described as being [A] qualitative [B] quantitative [C] both [D] neither 3. The correlation seen in the graph at the right would be best described as: [A] high positive correlation [B] low positive correlation [C] high negative correlation [D] low negative correlation 4. 62

65 5. 6. What is the total number of children in the families of the students in a ninth grade class? [A] 25 [B] 10 [C] 16 [D] 5 63

66 7. 8. Karen has grades of 90, 80, and 84 on three History exams. What grade must she obtain on the next test to have an average of exactly 88 for the four exams? [A] 60 [B] 88 [C] 98 [D] a. Which interval contains the median? b. Which interval contains the lower quartile? c. Which interval contains the upper quartile? 64

67 Neal kept track of the number of minutes it took him to assemble sandwiches at his restaurant. The information is in the table below. (a) Create a scatter plot using the table. (b) Describe the correlation: (c) Draw a trend line and determine the equation. (d) Based on the trend line, what is your prediction for the time it will take to assemble 14 sandwiches. 65

68 12. a) Complete the cumulative frequency table above. b) 66

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