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Math II Unit 4 Statistics Lessons

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Math II Unit 4 Statistics Lessons 1 MATHEMATICS II – Unit #4 Data Analysis and Probability/Statistics Day 1 E. Q. – How do I calculate the mean and standard deviation and use these measures to compare data sets? Standard – MM2D1. Using sample data, students will make informal references about population means and standard deviations. b. Understand and calculate the means and standard deviations of sets of data. c. Use means and standard deviations to compare data sets. Opening – Warm Up: Find the mean. Draw a box and whisker graph and label the lower quartile and upper quartile, and explain how to find the interquartile range Height (in inches) of selected students in a class: 58, 61, 66, 60, 68, 65, 64, 67, 70, 60 Mini lesson • Frayer Model of Vocabulary words: Review mean and interquartile range (IQR). • Introduce the following symbols: ∑ , x , σ, σ2 • Model, define, and explain new vocabulary: variance and standard deviation by working “Work Session Lesson 1” problems 1 & 2 Work Students work in pairs on “Work Session Lesson 1” session – problems 3 & 4 Closing – Student pairs are selected to share how they found their answers with the whole class. Ticket out the door – match formulas with statistical terms 2 Frayer Model for MEAN Definition Formula MEA MEANMEAN Example Your Example Frayer Model for INTERQUARTILE RANGE (IQR) Definition Formula INTERQUARTILEMEA RANGEMEAN Example Your Example 3 Frayer Model for VARIANCE Definition Formula VARIANCEMEA MEAN Example Your Example Frayer Model for STANDARD DEVIATION Definition Formula STANDARDMEA DEVIATIONMEAN Example Your Example 4 Math 2 Unit 4 Name Lesson 1 Date Period Find the mean, median, variance, standard deviation, and interquartile range of each data set. Show your work. OPENING 1.) 6, 22, 4, 15, 14, 8, 8 Mean = Median = Variance (σ2) = Standard Deviation (σ) = Interquartile Range (IQR) = 2.) 10, 15, 12, 20, 25, 22, 29 Mean = Median = Variance (σ2) = Standard Deviation (σ) = Interquartile Range (IQR) = 5 3.) 100, 150, 100, 130, 125, 135 Mean = Median = Variance (σ2) = Standard Deviation (σ) = Interquartile Range (IQR) = 4.) 15, 11, 18, 14, 14, 13, 17, 18 Mean = Median = Variance (σ2) = Standard Deviation (σ) = Interquartile Range (IQR) = 6 Work Session Lesson 1 Teacher Notes/Answer Key Typically, mean answers were rounded to the nearest hundredth and variance/standard deviation answers to the nearest thousandth if the answer was not a terminating decimal. 1.) 6, 22, 4, 15, 14, 8, 8 Æ 4, 6, 8, 8, 14, 15, 22 Mean = 77 ÷ 7 = 11 Standard Deviation = 5.831 Median = 8 IQR = 15 – 6 = 9 Variance = 34 2.) 10, 15, 12, 20, 25, 22, 28 Æ 10, 12, 15, 20, 22, 25, 29 Mean = 133 ÷ 7 = 19 Standard Deviation = 6.459 Median = 20 IQR = 25 – 12 = 13 Variance = 41.714 3.) 100, 150, 100, 130, 125, 135 Æ 100, 100, 125, 130, 135, 150 Mean = 740 ÷ 6 = 123.33 Standard Deviation = 18.181 Median = (125 + 130)÷ 2 = 127.5 IQR = 135 – 100 = 35 Variance = 1983,3334 ÷ 6 = 330.556 4.) 15, 11, 19, 14, 14, 13, 17, 18 Æ 11, 13, 14, 14, 15, 17, 18, 18 Mean = 120 ÷ 8 = 15 Standard Deviation = 2.525 Median = (14 + 15) ÷ 2 = 14.5 IQR = 17.5 – 13.5 = 4 Variance = 51 ÷ 8 = 6.375 7 Math 2 DAY 1 Name Unit 4 TICKET OUT THE DOOR Match the formula to the correct term by drawing a line. 1. Interquartile Range A. 2. Mean 3. Standard Deviation B. 4. Variance C. D. Q3 – Q1 Math 2 DAY 1 Name Unit 4 TICKET OUT THE DOOR Match the formula to the correct term by drawing a line. 1. Interquartile Range A. 2. Mean 3. Standard Deviation B. 4. Variance C. D. Q3 – Q1 8 Day 2 E. Q. – How do I calculate the mean and standard deviation and use these measures to compare data sets? Standard MM2D1. Using sample data, students will make – informal references about population means and standard deviations. b. Understand and calculate the means and standard deviations of sets of data. c. Use means and standard deviations to compare data sets. Opening – Warm-up: Write the formulas using new symbols for mean, interquartile range, variance, and standard deviation. Mini Lesson: • Have students reference their Frayer Model sheets for vocabulary from Lesson 1. • Using “Statistical Practice” Worksheet, model problem 1. Work Students work in pairs on “Statistical Practice” session – Worksheet problems 2,3,4 Closing – Students explain their work to the whole class. Homework: Outliers and Central Tendency 9 DAY 2 STATISTICAL PRACTICE NAME DATE PERIOD OPENING Definitions Review Write the formula or explain how to find each of the following statistical measures: MEAN MEDIAN MODE RANGE VARIANCE STANDARD INTERQUARTILE DEVIATION RANGE The following problems are adapted from Basic Statistical Analysis, 7th Edition, by Richard C. Sprinthall. Compute each of the seven statistical measures for each set of data. 1.) A group of seven university students was randomly selected and asked to indicate the number of study hours each put in before taking a major exam. The data are as follows: Hours of Student Study 1 40 2 30 3 35 4 5 5 10 6 15 7 25 WORK SESSION 10 2.) The grade-point averages for the seven university students selected above were computed. The data are as follows: Student GPA 1 3.75 2 3.00 3 3.25 4 1.75 5 2.00 6 2.25 7 3.00 3.) A researcher investigating a new product for clearing up acne selects a random sample of 10 teenagers, gives them the facial product to use and asks them to report back how many days it took for the facial condition to clear up. The results (in days) were as follows: 20, 8, 10, 14, 15, 14, 12, 11, 14, 13. 4.) A clinical psychologist is interested in assessing the prevalence of MDD (Major Depressive Disorders) among a group of fourth-grade students. A random sample of 13 students was selected and given the Children’s Depression Inventory (CDI), a self- report instrument that measures levels of depression. Scores above 13 are said to indicate a major depressive disorder. The scores were as follows: 8, 10, 11, 7, 13, 4, 8, 7, 9, 3, 15, 10, 10. 11 STATISTICAL PRACTICE TEACHER NOTES/ANSWER KEY Note: The emphasis of Math 2 is on using means and standard deviations, but the students were exposed to median, quartiles, and interquartile range in Math 1 (MM1D3a). They had previously also dealt with mean, median and mode in 7th grade (M7D1c) as well as range, quartiles, and interquartile range (M7D1d). It is the teacher’s discretion whether to compute every statistical measure or whether to focus only on those emphasized in Math 2. 1.) Data were: 40, 30, 35, 5, 10, 15, 25 Æ 5, 10, 15, 25, 30, 35, 40 Mean = 160 ÷ 7 = 22.86 Variance = 1042.8572 ÷ 7 = 148.9796 Median = 25 Std. Dev. = 12.206 Mode = no mode IQR = 35 – 10 = 25 Range = 40 – 5 = 35 2.) Data were: 3.75, 3.00, 3.25, 1.75, 2.00, 2.25, 3.00 Æ 1.75, 2.00, 2.25, 3.00, 3.00, 3.25, 3.75 Mean = 19 ÷ 7 = 2.71 Variance = 3.1787 ÷ 7 = 0.4541 Median = 3.00 Std. Dev. = 0.6739 Mode = 3.00 IQR = 3.25 – 2.00 = 1.25 Range = 3.75 – 1.75 = 2.00 3.) Data were: 20, 8, 10, 14, 15, 14, 12, 11, 14, 13. Æ 8, 10, 11, 12, 13, 14, 14, 14, 15, 20 Mean = 131 ÷ 10 = 13.1 Variance = 94.9 ÷ 10 = 9.49 Median = (13 + 14) ÷ 2 = 13.5 Std. Dev. = 3.081 Mode = 14 IQR = 14 – 11 = 3 Range = 20 – 8 = 12 4.) Data were: 8, 10, 11, 7, 13, 4, 8, 7, 9, 3, 15, 10, 10. Æ 3, 4, 7, 7, 8, 8, 9, 10, 10, 10, 11, 13, 15 Mean = 115 ÷ 13 = 8.85 Variance = 129.6925 ÷ 13 = 9.9763 Median = 9 Std. Dev. = 3.159 Mode = 10 IQR = 10.5 – 7 = 3.5 Range = 15 – 3 = 12 12 DAY 2 HOMEWORK Outliers and Central Tendency Connect to Prior Learning The puzzle below can be used as a way to review finding measures of central tendency and the effect of an outlier on the measures of central tendency. Questions to Start the Lesson In Questions 1–10, use the data set to answer the questions. Then find the corresponding letter in the table to the left to answer the riddle. What did Watson say to Holmes? 2, 3, 4, 5, 6, 8, 9, 9, 17 1. Find the mean. 2. Find the median. 3. Find the mode. 4. Find the standard deviation. 5. Find the range. 6. Which value is an outlier? In Questions 7–11, find the measures of central tendency after removing the outlier. 7. Find the mean. 8. Find the median. 9. Find the range. 10. Find the standard deviation. 13 Day 3 E. Q. – How do I calculate the mean and standard deviation and use these measures to compare data sets? Standard MM2D1. Using sample data, students will make – informal references about population means and standard deviations. b. Understand and calculate the means and standard deviations of sets of data. c. Use means and standard deviations to compare data sets. Opening Warm Up: Write two sentences using the word – “deviation”. How would you define “deviation”? Mini lesson: Work and explain the OPENING on Performance Task 1 Work Students work in groups of 3 on the WORK session – SESSION on Performance Task 1 Closing – Students share out and explain their answers to Performance Task 1. Students review the vocabulary: Mean deviation, Variance, and Standard Deviation.
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