Samples and Populations: Making Comparisons and Predictions Name: Per: Investigation 1: Making Sense of Samples Date Learning Target/s Classwork Homework Self-Assess Your Learning Mon, Apr. 18 Calculate measures of center and measures of variability. Pg. 2-3: SP 1.1 Using Center and Spread, Part 1 Tues, Apr. 19 Use measures of center and measures of variability to compare data sets. Pg. 5-6: SP 1.1 Weds, Apr. 20 Thurs, Apr. 21 Use the MAD to compare samples. Use relative frequencies to compare samples. Using Center and Spread, Part 2 Pg. 8-9: SP 1.2 Using MAD to Compare Samples Pg. 11-12: SP 1.3 Categorical Data Pg. 14-16: SP 1.4 Using the IQR to Compare Samples Pg. 4 SP 1.1, Part 1 Zaption Pg. 7 SP 1.1, Part 2 Zaption Fri, Apr. 22 Use the interquartile range Vocabulary Earth Day (IQR) to compare samples. Quizizz Mon, Apr. 25 Pg. 17 SP Tues, Apr. 26 Inv. 1 Assess understanding Investigation 1 learning targets. Check Up 1 Pg. 18 SBAC Review 4 Zaption Pg. 10 SP 1.2 Zaption Pg. 13 SP 1.3 Zaption 1.4 Zaption CCSS.MATH.CONTENT.7.SP.B.3 Informally assess the degree of visual overlap of two numerical data distributions with similar variabilities, measuring the difference between the centers by expressing it as a multiple of a measure of variability. For example, the mean height of players on the basketball team is 10 cm greater than the mean height of players on the soccer team, about twice the variability (mean absolute deviation) on either team; on a dot plot, the separation between the two distributions of heights is noticeable. CCSS.MATH.CONTENT.7.SP.B.4 Use measures of center and measures of variability for numerical data from random samples to draw informal comparative inferences about two populations. For example, decide whether the words in a chapter of a seventh-grade science book are generally longer than the words in a chapter of a fourthgrade science book. Parent/Guardian Signature: Due: 1
SP 1.1, Part 1: Comparing Performances Using Center and Spread What is variability? Measures of Center: Mean and Median How do you calculate the mean? How do you calculate the median? Mean: 5, 8, 10, 12, 7 Median: 5, 8, 10, 12, 7 Mean: 50, 45, 37, 40, 45, 60 Median: 50, 45, 37, 40, 45, 60 A. 1. Find the mean of Jun s scores (80, 60, 100). Show your calculations. 2. Find the median of Jun s scores (80, 60, 100). Show how you found it. 3. Find the mean of Mia s scores (75, 80, 85). Show your calculations. 4. Find the median of Mia s scores (75, 80, 85). Show how you found it. 5. Use the measures of center you found in parts 1 and 2. Compare Jun s and Mia s test performance. Write at least two complete sentences. 2
Measures of Variability: Range and Mean Absolute Deviation How do you calculate the range? How do you calculate the mean absolute deviation (MAD)? Range: 5, 8, 10, 12, 7 MAD: 5, 8, 10, 12, 7 B. 1. Determine the range of Jun s test scores (80, 60, 100). Show your calculations. 2. Determine the mean absolute deviation (MAD) of Jun s test scores (80, 60, 100). Show your calculations. 3. Determine the range of Mia s test scores (75, 80, 85). Show your calculations. 4. Determine the MAD of Mia s test scores (75, 80, 85). Show your calculations. 5. Use the measures of spread you found in parts 1 and 2. Compare Jun s and Mia s test performances. Write at least two complete sentences. 3
Homework: SP 1.1, Part 1 Complete and correct with Zaption Diver Dive 1 Dive 2 Dive 3 Dive 4 Dive 5 Jarrod 8.5 8.1 6.4 9.5 10 Pascal 9.3 7.5 8 8.5 9.2 1. Find the measures of center for the two divers. Student Median Mean Jarrod Pascal 2. Compare the measures of center for the two divers. Write at least two complete sentences. 3. Find the measures of variability for the two divers. Student Range MAD Jarrod Pascal 4. Compare the measures of variability for the two divers. Write at least two complete sentences. 4
SP 1.1, Part 2: Comparing Performances Using Center and Spread C. Think about when you looked at Jun and Mia s test scores from the first quarter (on pages 2 and 3) and analyzed the measures of center and variability. Do you have enough data to make any general statements about Jun s or Mia s overall math test performance? Explain. Write at least two complete sentences. D. Jun s score mid-year: 80, 60, 100, 80, 80, 80 Mia s scores mid-year: 75, 80, 85, 80, 80, 100 1. Find the median of Jun s data (80, 60, 100, 80, 80, 80). Show how you found it. 2. Find the median of Mia s data (75, 80, 85, 80, 80, 100). Show how you found it. 3. Find the mean of Jun s data(80, 60, 100, 80, 80, 80). Show your calculations. 4. Find the mean of Mia s data (75, 80, 85, 80, 80, 100). Show your calculations. 5. Use each measure of center (median and mean) to compare Jun s scores and Mia s scores. Write at least two complete sentences. 5
6. Find the range of Jun s data (80, 60, 100, 80, 80, 80). Show your calculations. 7. Find the range of Mia s data (75, 80, 85, 80, 80, 100). Show your calculations. 8. Find the MAD of Jun s data (80, 60, 100, 80, 80, 80). Show your calculations. 9. Find the MAD of Mia s data (75, 80, 85, 80, 80, 100). Show your calculations. 10. Use each measure of variability (range and MAD) to compare Jun s scores and Mia s scores. Write at least two complete sentences. 6
Homework: SP 1.1, Part 2 Complete and correct with Zaption 1. What are the measures of center? What do they tell us about a data set? 2. What are the measures of variability? What do they tell us about a data set? 3. Summarize the statistics you found in class today (see pages 5 and 6): Student Median Mean Range MAD Jun Mia 4. Decide whether you agree or disagree with each statement below. Use the statistics you found in the earlier questions. Explain your reasoning. Write at least two complete sentences for each statement. a. One student is a stronger math student than the other. b. One student is more consistent than the other. c. The two students perform equally well on math tests. d. You can make better comparisons using the larger data set. 7
SP 1.2: Using MAD to Compare Samples Which team is the most successful and deserves to win the prize? A. Make a line plot of each team s data. Find the total money raised, mean, and MAD of each data set. Team Line Plot Total $ Raised 1 Mean (Add ) MAD (Add Lines) 2 3 4 5 6 8
B. The Hiking Club s organizers must decide which team is awarded the prize. Each organizer has a different strategy for determining the most successful fundraising team. For each strategy below, explain whether or not the strategy helps determine the most successful team. If the strategy helps determine the most successful team, determine who will win the prize. 1. Bianca: For each team, just add up all the money raised by its members. Then compare to the team totals. 2. Gianna: Find the mean number of dollars raised by each team. Then compare the team averages. 3. Jonah: Compare the money raised by each member to the team s average. On average, how far does each member s amount differ from the team s mean amount? For each team, find the MAD. Then compare the MADs of the six teams. C. In Question A, you made line plots of the six sets of data. In Question B, you found the MAD of each distribution. The dot plot shows Team 1 s fundraising amounts. The lines indicate the distances of one MAD and two MADs from the mean on either side. Count the data points located closer than, but not including, the distance of one MAD from the mean. The indicates the mean, 35. 1. How many of Team 1 s data values are located within one MAD (both less than and greater than the mean)? Write this number as a percent. 2. How many of Team 1 s data values are located within two MADs (both less than and greater than the mean)? Write this number as a percent. 3. How many of Team 1 s data values are more than two MADs away from the mean? Write this number as a percent. 9
Homework: SP 1.2 Complete and correct with Zaption Complete the table. For each team: a. On the line plot, mark the mean with a triangle, and then mark the location of one and two MADs from the mean with lines (the mean and MAD of each team are included in the table already). b. Find the percent of values within one MAD of the mean, two MADs of the mean, and greater than two MADs from the mean. Team Line Plot Mean MAD Percent of Data Within 1 MAD 2 MADs >2 MADs 1 2 3 4 5 6 10
SP 1.3: Distinguishing Categorical Data from Numerical Data Categorical Data Numerical Data The sample sizes of Internet respondents and 7 th graders are different. You can use relative frequencies frequencies based on percentages to compare samples of different sizes. How do you find relative frequencies? Ex: What is the frequency of people who prefer to sit on the front of the roller coaster in each sample? Roller Coaster Seating Preferences Preference Votes from Relative Votes from Internet Frequency 7 th Graders Front 97 27 Relative Frequency Votes From Our Class Relative Frequency Middle 50 22 Back 18 14 Total Votes 165 63 Other Roller Coaster Preferences Preference Votes from Relative Votes from Internet Frequency 7 th Graders Airtime 88 31 Relative Frequency Votes From Our Class Relative Frequency Height 36 24 Inversions 59 29 Smoothness 39 12 Speed 105 57 Total Votes 327 153 11
B. For each survey question, make bar graphs of the three data sets. Where do you like to sit on a roller coaster? Internet 7 th Graders Our Class Which of the following roller coaster characteristics do you prefer? You may choose more than one. Internet 7 th Graders Our Class C. Which measure/s of center mean, median, or mode can you use to describe these results? D. For each survey question, write two statements comparing results from the three data sets. Use complete sentences. 12
Homework: SP 1.3 Complete and correct with Zaption This homework assignment is related to our classwork today. Look back at pages 11 and 12 to help you. 1. Write two statements to summarize the data collected from the Roller Coaster Survey. Use complete sentences. 2. How are the summaries useful? 3. Suppose 400 people ride a roller coaster in one day. How many of them would you predict want to sit at the front? Explain. 4. The following question was asked in a survey: What is your favorite amusement park ride roller coaster, log ride, ferris wheel, or bumper cars? The table below shows the results from an internet survey and from 7 th grade students at East Jr. High and West Jr. High. Favorite Ride Votes from Internet Relative Frequency Votes from East Jr. High Relative Frequency Votes from West Jr. High Roller 92 42 36 Coaster Log Ride 26 31 14 Relative Frequency Ferris Wheel Bumper Cars Total Votes 22 3 6 20 4 4 160 80 60 a. Find the relative frequencies of the data and them to the table. b. Write three or more statements comparing the data sets. Use complete sentences. 13
Steel-Frame Rollercoasters SP 1.4: Using the IQR to Compare Samples A. How might you decide which are faster, steel-frame roller coasters or wood-frame roller coasters? Explain. 22, 22, 35, 35, 35, 35, 40, 42, 45, 45, 48, 48, 50, 50, 54, 55, 55, 60, 61, 63, 66, 66, 70, 70, 73, 75, 76, 80, 85, 90 MEASURES OF CENTER: Mean: Mode/s: Median: Lower Quartile (LQ): Upper Quartile (UQ): MEASURES OF VARIABILITY: Minimum: Maximum: Range: IQR: Outlier/s: Box and Whisker Plot: Line Plot: 14
Wood-Frame Rollercoasters 25, 32, 35, 44, 45, 45, 47, 50, 50, 50, 50, 51, 51, 51, 51, 55, 55, 55, 56, 56, 60, 60, 60, 62, 62, 62, 62, 65, 65, 66 MEASURES OF CENTER: Mean: Mode/s: Median: Lower Quartile (LQ): Upper Quartile (UQ): MEASURES OF VARIABILITY: Minimum: Maximum: Range: IQR: Outlier/s: Box and Whisker Plot: Line Plot: B. Are steel-frame coasters faster than wood-frame coasters? Explain your reasoning based on statistics. Use at least three complete sentences. 15
C. Charlie and Rosa wrote the reports below. They used the two distributions of data to compare steel-frame roller coasters and wood-frame roller coasters. Do you agree with Charlie or with Rosa? Explain your reasoning. Use at least three complete sentences. Extra Challenge: Calculate the MAD for the roller coaster data sets. 16
Homework: SP 1.4 Complete and correct with Zaption 1. Use the dot plots below to answer the questions for each distribution. a. Draw lines on the dot plots to show one and two MADS away from the mean. b. How many roller coasters have speeds within one MAD of the mean (both less than and greater than)? Write this number as a percent. Steel-Frame: Wood-Frame: c. How many roller coasters have speeds within two MADs of the mean (both less than and greater than)? Write this number as a percent. Steel-Frame: Wood-Frame: d. How many roller coasters have speeds more than two MADs away from the mean? Write this number as a percent. Steel-Frame: Wood-Frame: e. Based on the statistics, which roller coasters go faster? Explain your reasoning. 17
SBAC Practice Test Part 4 Score: / 3 (Complete and correct with Zaption)? Question and Answer Correct Answer 1 A representative sample of 50 students from a high school is surveyed. Each student is asked what science course he or she is taking. Choose True or False to indicate whether each statement is valid based on the survey results. 2 The spinner has 8 equal-sized sections each labled 1, 2,3, or 4. The arrow on the spinner is spun. Match the outcomes (landing on a 1, 2, 3, 4) to the category that correctly describes the probability of the outcome. 3 Consider the equation. Identify two expressions that are equivalent to w in the shaded section. 18