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Lesson Menu Five-Minute Check (over Lesson 11–1) CCSS Then/Now New Vocabulary Key Concept: Symmetric and Skewed Distributions Example 1: Real-World Example: Describe a Distribution Using a Histogram Key Concept: Box-and-Whisker Plots as Distributions Example 2: Describe a Distribution Using a Box-and- Whisker Plot Example 3: Compare Data Using Histograms Example 4: Compare Data Using Box-and-Whisker Plots

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Over Lesson 11–1 5-Minute Check 1 A.Survey; members of the sample are observed and asked their opinions. B.Experiment; members of the sample are observed and affected by the study. C.Observational study; members of the sample are observed and unaffected by the study. D.Experiment; members of the sample are treated and affected by the study. Determine whether the situation calls for a survey, an experiment, or an observational study. Explain your reasoning. MOVIES A production studio played a movie for a test audience and watched their reactions.

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Over Lesson 11–1 5-Minute Check 2 A.Survey; members of the sample are observed and unaffected by the study. B.Survey; members of the sample are asked for their opinions. C.Observational study; members of the sample are observed and unaffected by the study. D.Experiment; members of the sample are treated and affected by the study. Determine whether the situation calls for a survey, an experiment, or an observational study. Explain your reasoning. AUTHORS At a library, every 10th person is asked some questions about their favorite author.

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Over Lesson 11–1 5-Minute Check 3 A.Biased; the question is confusing and wordy. B.Biased; the question causes a strong reaction. C.Biased; the question encourages a certain response. D.unbiased Determine whether the survey question is biased or unbiased. If biased, explain your reasoning. Shouldn’t Megan Fox win the Best Actress award this year?

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Over Lesson 11–1 5-Minute Check 4 A.Biased; the question is confusing and wordy. B.Biased; the question causes a strong reaction. C.Biased; the question encourages a certain response. D.unbiased Determine whether the survey question is biased or unbiased. If biased, explain your reasoning. How many siblings do you have?

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Over Lesson 11–1 5-Minute Check 5 MANAGERS A manager of a company wants to determine if her employees would prefer to work four 10-hour days as opposed to five 8-hour days each week. State the objective of the survey, suggest a population, and write two unbiased survey questions.

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Over Lesson 11–1 5-Minute Check 5 A.objective: to determine the work preferences of the employees; population: all employees; sample survey questions: Are you satisfied with working five 8-hour days each week? Would you be willing to try to work four 10-hour days? B.objective: to determine the work preferences of the employees; population: the employees who responded to the survey; sample survey questions: Are you satisfied with working five 8- hour days each week? Would you be willing to try to work four 10-hour days? C.objective: to determine the work preferences of the employees; population: the employees who want to work four 10-hour days; sample survey questions: Are you satisfied with working five 8- hour days each week? Would you be willing to try to work four 10-hour days? D.objective: to determine the work preferences of the employees; population: the sample; sample survey questions: Are you satisfied with working five 8-hour days each week? Would you be willing to try to work four 10-hour days?

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CCSS Content Standards S.IC.1 Understand statistics as a process for making inferences about population parameters based on a random sample from that population. Mathematical Practices 1 Make sense of problems and persevere in solving them.

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Then/Now You calculated measures of central tendency and variation. Use the shapes of distributions to select appropriate statistics. Use the shapes of distributions to compare data.

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Vocabulary distribution negatively skewed distribution symmetric distribution positively skewed distribution

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Concept

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Example 1 Describe a Distribution Using a Histogram PRESENTATIONS Ms. Shroyer’s students each gave a presentation as part of their class project. The length of each presentation is shown in the table. A. Use a graphing calculator to create a histogram. Then describe the shape of the distribution.

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Example 1 Answer: The majority of the data are on the right side of the distribution, so the distribution is negatively skewed. Describe a Distribution Using a Histogram First, press and enter each data value. Then, press [STAT PLOT] and choose „. Finally, adjust the window to the dimensions shown.

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Example 1 Describe a Distribution Using a Histogram PRESENTATIONS Ms. Shroyer’s students each gave a presentation as part of their class project. The length of each presentation is shown in the table. B. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice.

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Example 1 Answer: The range is 7 to 23 minutes. The median is 17 minutes, and half of the times are between 13 and 19.5 minutes. Describe a Distribution Using a Histogram The distribution is skewed, so use the five-number summary to describe the center and spread. Press and scroll down to view the five-number summary. The range is 7 to 23 minutes. The median is 17 minutes, and half of the times are between 13 and 19.5 minutes.

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Example 1 A.mean: 134.75, standard deviation: 30.3; skewed distribution B.median: 137, range: 70 to 195, half of the data between 117.5 and 149.5; skewed distribution C.mean: 134.75, standard deviation: 30.3; symmetric distribution D.median: 137, range: 70 to 195, half of the data between 117.5 and 149.5; symmetric distribution PRICING Eddie looked up prices for floor speakers for his basement. The prices are shown in the table. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice.

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Concept

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Example 2 Describe a Distribution Using a Box-and- Whisker Plot A. WAGES The hourly wages for a random sample of employees of a restaurant are shown in the table. Use a graphing calculator to create a box-and- whisker plot. Then describe the shape of the distribution.

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Example 2 Describe a Distribution Using a Box-and- Whisker Plot Answer: The right whisker is longer than the other and the median is to the left of the center, so the distribution is positively skewed. Enter the data as L1. Press [STAT PLOT] and choose ﬂ. Adjust the window to the dimensions shown.

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Example 2 Describe a Distribution Using a Box-and- Whisker Plot B. WAGES The hourly wages for a random sample of employees of a restaurant are shown in the table. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice. Answer: The distribution is skewed, so use the five- number summary. The range is $6.50 to $11.25. The median is about $7.88, and half of the data are between $7.25 and $9.00.

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Example 2 EXPERIENCE The number of years of playing experience for each player on an over 30 recreational soccer team are shown in the table. Describe the center and spread of the data using either the mean and standard deviation or the five-number summary. Justify your choice. A.mean: 4.1, standard deviation: 3.5; skewed distribution B.median: 3, range: 0 to 12, half of the data between 1 and 7; skewed distribution C.mean: 4.1, standard deviation: 3.5; symmetric distribution D.median: 3, range: 0 to 12, half of the data between 1 and 7; symmetric distribution

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Example 3 Compare Data Using Histograms A. GAMES Tyler and Jordan are working through several brainteasers on the computer. The time in minutes that it took to complete each game is shown. Use a graphing calculator to create a histogram for each data set. Then describe the shape of each distribution.

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Example 3 Compare Data Using Histograms Answer: Tyler, positively skewed; Jordan, symmetric

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Example 3 Compare Data Using Histograms B. GAMES Tyler and Jordan are working through several brainteasers on the computer. The time in minutes that it took to complete each game is shown. Compare the distributions using either the means and standard deviations or the five- number summaries. Justify your choice.

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Example 3 Compare Data Using Histograms Answer: Sample answer: One distribution is symmetric and the other is skewed, so use the five-number summaries. The median for both sets is 4.35 but 50% of Tyler’s times occur between 3.45 and 5.15, while 50% of Jordan’s times occur between 3.75 and 5.4. The smaller interquartile range for Jordan may suggest that she was slightly more consistent than Tyler.

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Example 3 GAMES Mr. Cline’s 1st and 2nd Period classes tracked the amount of time per week they spent on their favorite Web site. The times in minutes are shown. Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. A.2nd Period had a slightly higher median and the ranges were almost the same. The distributions are very similar. B.2nd Period had a higher mean and greater deviation. 1st Period is a little more consistent. C.2nd Period had a higher mean and greater deviation. 2nd Period is a little more consistent. D.2nd Period had a slightly higher median and the ranges were almost the same. 2nd Period is a little more consistent.

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Example 4 Compare Data Using Box-and-Whisker Plots A. TEMPERATURES The daily high temperatures over a 20-day period for two cities are shown. Use a graphing calculator to create a box-and-whisker plot for each data set. Then describe the shape of each distribution.

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Example 4 Compare Data Using Box-and-Whisker Plots Answer: Both distributions are symmetric. Enter the Clintonville temperatures as L1. Graph these data as Plot1 by pressing [STAT PLOT] ENTER ENTER and choosing ﬂ. Enter the Stockton temperatures as L2. Graph these data as Plot2 by pressing 2ND [STAT PLOT] ▼ ENTER ENTER and choosing ﬂ. For Xlist, enter L2. Adjust the window to the dimensions shown.

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Example 4 Compare Data Using Box-and-Whisker Plots B. TEMPERATURES The daily high temperatures over a 20-day period for two cities are shown. Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice.

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Example 4 Compare Data Using Box-and-Whisker Plots Answer: The distributions are symmetric, so use the means and standard deviations. The mean temperature for Clintonville is about 63.15° with standard deviation of about 5.40°. The mean temperature for Stockton is about 63.05° with standard deviation of about 1.76°. The average temperatures for both cities are about the same, but the lower standard deviation for Stockton means that the temperatures there are more consistently near 63° than at Clintonville.

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Example 4 SUMMER CAMP The number of participants for two sports at a summer camp for the past 15 sessions is shown. Compare the distributions using either the means and standard deviations or the five-number summaries. Justify your choice. A.The mean number for baseball was almost twice the mean for soccer. The distributions are skewed. B.The standard deviation of the number for baseball was almost three times the standard deviation for soccer. The distributions are symmetric. C.The median number for baseball was 23 more than the median for soccer. The distributions are skewed. D.The median number for baseball was 23 more than the median for soccer. The distributions are symmetric.

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End of the Lesson

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