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Unit 4: Describing Data

Unit 4: Describing Data. Unit 4 Review. Summarize, represent, and interpret data on a single count or measurement variable Summarize, represent, and interpret data on two categorical and quantitative variables Interpret linear models. Unit 4: Lesson 1.

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Unit 4: Describing Data

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  1. Unit 4: Describing Data

  2. Unit 4 Review • Summarize, represent, and interpret data on a single count or measurement variable • Summarize, represent, and interpret data on two categorical and quantitative variables • Interpret linear models

  3. Unit 4: Lesson 1 Summarize, represent, and interpret data on a single count or measurement variable MCC9-12.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).★ MCC9-12.S.ID.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 data sets.★ (Standard deviation is left for Advanced Algebra, use MAD as a measure of spread.) MCC9-12.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).★

  4. MCC9-12.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).★ 5 Number Summary Dataset: 5, 9, 3, 16, 8, 5, 2, 5, 6, 7, 5, 2, 15, 4 Min: Q1: Median: Q3: Max: 4 5 Put them in order. 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 16 2 8 Let’s make a Box and Whisker!! 16 2 8 4 5

  5. MCC9-12.S.ID.1 Represent data with plots on the real number line(dot plots, histograms, and box plots).★ Dataset: 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 This is a box plot! (boxand whisker) Can we compare the range to the IQR? Q3 – Q1 8 – 4 4 max - min 16 – 2 14 What does that mean? There are outliers Your IQR is a small percentage of the overall data.

  6. MCC9-12.S.ID.1 Represent data with plots on the real number line(dot plots, histograms, and box plots).★ Can we compare the these two? IQR: Median: Range: MCC9-12.S.ID.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 data sets.★ (Standard deviation is left for Advanced Algebra, use MAD as a measure of spread.)

  7. Try this one Speed of light True speed

  8. MCC9-12.S.ID.1 Represent data with plots on the realnumberline(dot plots, histograms, and box plots).★ Dataset: 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 This is an example of a dot plot outliers

  9. MCC9-12.S.ID.1 Represent data with plots on the realnumberline(dot plots, histograms, and box plots).★ Dataset: 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 2, 2, 3, 4, 5, 5, 5, 5, 6, 7, 8, 9, 15, 16 A histogramis a bar graph with no spaces between the bars. Let’s make it a histogram Step 1: Create boxes Step 2: Shade the boxes

  10. Types for Histograms Histogram Symmetric Histogram – skewed to the right Histogram – skewed to the left

  11. Histogram Symmetric • Normal. A common pattern is the bell–shaped curve known as the “normal distribution.” • In a normal distribution, points are as likely to occur on one side of the average as on the other.

  12. Histogram – skewed to the right Median < Mean • Skewed.The skewed distribution is asymmetrical because a natural limit prevents outcomes on one side. (These distributions are called right–skewedor left–skewedaccording to the direction of the tail.) • The distribution’s peak is off center toward the limit and a tail stretches away from it. • Examples, of natural limits are holes that cannot be smaller than the diameter of the drill bit or call-handling times that cannot be less than zero. Histogram – skewed to the left Median > Mean

  13. Median < Mean Median > Mean 2 2.047 4 3.904 Right Skewed Left Skewed 1 2 3 4 5 1 2 3 4 5 Data Set: 1, 1, 1, 1, 1, 1, 1, 1, 2, 2, 2, 2, 2, 3, 3, 3, 3, 4, 4, 4, 5 Data Set: 1, 2, 2, 3, 3, 3, 3, 4, 4, 4, 4, 4, 5, 5, 5, 5, 5, 5, 5, 5, 5

  14. What is a Frequency Table? A Frequency table is a table that lists each item in a data set with the number of times it occurs.

  15. Construct a Frequency Table (tally sheet) 7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10 Enter the data value into the 1st column

  16. Construct a Frequency Table (tally sheet) 7, 10, 10, 9, 8, 9, 7, 4, 3, 7, 10, 4, 8, 9, 6, 7, 10 Enter a tally for each entry.

  17. Construct a Frequency Table (tally sheet) Count the tallies and put the total for each value in the frequency column 1 2 1 4 2 3 4

  18. Construct a Frequency Table (tally sheet) We can find the percent in each row by dividing by the total. 1 6% 1/17=0.058 2 12% 2/17=0.117 1 6% 1/17=0.058 4 24% 4/17=0.235 2 12% 2/17=0.117 3 18% 3/17=0.176 4 24% 4/17=0.235 17

  19. Unit 4: Lesson 1 Summarize, represent, and interpret data on a single count or measurement variable MCC9-12.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).★ MCC9-12.S.ID.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 data sets.★ (Standard deviation is left for Advanced Algebra, use MAD as a measure of spread.)

  20. MCC9-12.S.ID.2 Use statistics appropriate to the shape of the data distribution to comparecenter (median, mean) and spread(interquartile range, standard deviation) of two or more different data sets.★ (Standard deviation is left for Advanced Algebra, use MAD as a measure of spread.) Range: 38 – 19 19 Range: 35 – 16 19 6 12

  21. Checking Understanding A science teacher recorded the pulse rates for each of the students in her classes after the students had climbed a set of stairs. She displayed the results, by class, using the box plots shown. Which class had the highest pulse rates after climbing the stairs? Class 3

  22. Unit 4: Lesson 1 Summarize, represent, and interpret data on a single count or measurement variable MCC9-12.S.ID.1 Represent data with plots on the real number line (dot plots, histograms, and box plots).★ MCC9-12.S.ID.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 data sets.★ (Standard deviation is left for Advanced Algebra, use MAD as a measure of spread.) MCC9-12.S.ID.3 Interpret differences in shape, center, and spread in the context of the data sets, accounting for possible effects of extreme data points (outliers).★ We’ve done We’ve done We’ve done briefly

  23. Unit 4: Lesson 2 Summarize, represent, and interpret data on two categorical and quantitative variables MCC9-12.S.ID.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.★ MCC9-12.S.ID.6 Represent data on two quantitative variables on a scatter plot, and describe how the variables are related.★ MCC9-12.S.ID.6a Fit a function to the data; use functions fitted to data to solve problems in the context of the data. Use given functions or choose a function suggested by the context. Emphasize linear, quadratic, and exponential models.★ MCC9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.★ MCC9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.★

  24. Vocabulary Categorical Variables are objects being studied are grouped into categories based on some qualitative trait • Examples: color, type of pet, gender, ethnic group, religious affiliation • Bar graphs and pie charts are frequently associated with categorical data. Quantitative Variables are objects being studied are grouped into categories based on anumericalvalue. • Examples: age, years of schooling, height, weight, test score • Box plots, dot plots, and histograms are used with quantitative data. • The measures of central tendency (mean, median, and mode) apply to quantitative data. Frequenciescan apply to both categorical and quantitative.

  25. MCC9-12.S.ID.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). Bivariate data consists of pairs of linked numerical (quantitate)observations, or frequencies of things in categories. • Numerical (quantitate)bivariate data can be presented as ordered pairs and in any way that ordered pairs can be presented: as a set of ordered pairs, as a table of values, or as a graph on the coordinate plane. • Categorical example: frequencies of gender and club memberships for 9th graders. Bivariate or two-way frequency chart • Each category is considered a variable; the categories serve as labels in the chart. • Two-way frequency charts are made of cells; number in each cell is the frequency of things

  26. MCC9-12.S.ID.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). two-way frequency chart 12/ 135 = 8%

  27. MCC9-12.S.ID.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). If no person or thing can be in more than one category per scale, the entries in each cell are called joint frequencies. The frequencies in the cells and the totals tell us about the percentages of students engaged in different activities based on gender. 100% 64% 36% 53% 47% 84% 16% 44% 56% 80% 20% 58% 42% 100%

  28. To find the percentages, divide each number by 135 (the total) Conditional frequenciesare not usually in the body of the chart, but can be readily calculated from the cell contents. Example: conditional frequency would be the percent of females that are in the chorus compared to the total number females in some type of club. 17 of the 57 females are in the chorus, so 29.8%. frequency = %

  29. There is also what we call marginal frequencies in the bottom and right margins (grayed cells). These frequencies lack one of the categories. Bottom: represent percent of males and females in the school population. Right: represent percent of club membership.

  30. Warm Up 10.17 Write the following points in order. Find the median point Find the Q1 and Q3 Find the BEST FIT line Median Q1 Q3

  31. MCC9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.★ Step 1: Plot points Step 2: Find the median *order points first* Step 3: Find Q1 and Q3 Step 4: Find the Best Fit line Step 5: Find the equation of the Best Fit line (1, 1) (3,1) (5,3) (6,5) (2, 2) (3, 3) (5,5) (7, 4) (2,3) (4, 4) (5,6) (7,6) (2,4) (4,5) (6, 3) (7,8) Use the same formula Use y = mx + b Median is between these two points (2, 4) (3, 1) (2.5, 2.5) This line hits 5 points (4, 5) (5, 3) (4.5, 4) This line hits 3 points This line hits approx. 1 points Do the same thing for Q3. Find approximate lines that go through two of the three points we have found. Use two scatter point on the line to find the slot Best Fit line goes through median and Q1

  32. MCC9-12.S.ID.6c Fit a linear function for a scatter plot that suggests a linear association.★ Step 1: Plot points Step 2: Find the median *order points first* Step 3: Find Q1 and Q3 Step 4: Find the Best Fit line Step 5: Find the equation of the Best Fit line Use two scatter point on the line to find the slot Use the same formula Use y = mx + b (1, 1) AND (2,2) y = mx + b 2 = (1)(2) + b 2 = 2 + b 0 = b So… y = 1x + 0 y = x = m Use either point to plug into slope intercept and solve for b.

  33. You try Find median Find Q1 and Q3 Approximate the BEST fit line Median 19 total points 10th point is the median Q1 Q1 is between 4th and 5th point Q3 Q3 is between 14th and 15th point

  34. You try Find median Find Q1 and Q3 Approximate the BEST fit line Median 19 total points 10th point is the median Q1 Q1 is between 4th and 5th point Q3 Q3 is between 14th and 15th point

  35. MCC9-12.S.ID.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.★ • If no person or thing can be in more than one category per scale, the entries in each cell are called joint frequencies. • Frequencies that lack one of the categoriesare considered marginal frequencies. MCC9-12.S.ID.6b Informally assess the fit of a function by plotting and analyzing residuals.★

  36. Homework Questions 60% 40% 100%

  37. Checking Understanding Peter went bowling, Monday to Friday, two weeks in a row. He only bowled one game each time he went. He kept track of his scores below. Week 1: 70, 70, 70, 73, 75 Week 2: 72, 64, 73, 73, 75 What is the best explanation of why Peter’s Week 2 mean score was lower than his Week 1 mean score? A. Peter received the same score three times in Week 1. B. Peter had one very bad score in Week 2. C. Peter did not improve as he did the first week. D. Peter had one very good score in Week 1. B

  38. Unit 4: Lesson 3 Interpret linear models MCC9-12.S.ID.7 Interpret the slope (rate of change) and the intercept (constant term) of a linear model in the context of the data.★ MCC9-12.S.ID.8 Compute (using technology) and interpret the correlation coefficient of a linear fit.★ MCC9-12.S.ID.9 Distinguish between correlation and causation.★

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