Grade 6 Supporting Idea 6: Data Analysis

1. Grade 6 Supporting Idea 6:Data Analysis

10. Grade 6 Supporting Idea: Data Analysis • MA.6.S.6.1 Determine the measures of central tendency (mean, median, and mode) and variability (range) for a given set of data. • MA.6.S.6.2 Select and analyze the measures of central tendency or variability to represent, describe, analyze and/or summarize a data set for the purposes of answering questions appropriately.

20. FAIR GAME: Prerequisite Knowledge • MA.3.S.7.1: Construct and analyze frequency tables, bar graphs, pictographs, and line plots from data, including data collected through observations, surveys, and experiments. • MA.5.S.7.1: Construct and analyze line graphs and double bar graphs.

21. FAIR GAME: Prerequisite Knowledge

27. Skills Trace • Add whole numbers, fractions, and decimals • Divide whole numbers, fractions, and decimals • Compare and order whole numbers, fractions, and decimals • Add whole numbers, fractions, and decimals • Divide whole numbers, fractions, and decimals • Compare whole numbers, fractions, and decimals • Subtract whole numbers, fractions, and decimals

28. Measures of Center mean median mode

29. MODEL: FINDING THE MEDIAN Find the median of 2, 3, 4, 2, 6. Participants will use a strip of grid paper that has exactly as many boxes as data values. Have them place each ordered data value into a box. Fold the strip in half. The median is the fold.

30. MODEL: FINDING THE MEAN • Arrange interlocking/Unifix cubes together in lengths of 3, 6, 6, and 9. • Describe how you can use the cubes to find the mean, mode, and median. • Suppose you introduce another length of 10 cubes. Is there any change in i) the mean, ii) the median, iii) the mode?

31. MODEL: FINDING THE MEAN

32. Thinking about measures of center The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 n n 6 15

33. Thinking about measures of center The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 n n 6 15

34. Thinking about measures of center The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 a b 6 15

35. Thinking about measures of center The median of five numbers is 15. The mode is 6. The mean is 12. What are the five numbers? 6 a b 6 15

36. Missing Observations: Mean Here are Jane’s scores on her first 4 math tests: • 82 75 79 What score will she need to earn on the fifth test for her test average (mean) to be an 80%?

37. Missing Observations: Mean Here are Jane’s scores on her first 4 math tests: • 82 75 79 There is one more test. Is there any way Jane can earn an A in this class? (Note: An “A” is 90% or above) What measure of center are we asking students to consider?

38. Missing Observations: Mean Here are Jane’s scores on her first 4 math tests: • 82 75 79 There is one more test. Is there any way Jane can earn an A in this class? (An “A” is 90% or above)

39. Missing Observations: Median Here are Jane’s scores on her first 4 math tests: • 82 75 79 What score will she need to earn on the fifth test for the median of her scores to be an 80%? • 79 80 82

40. Missing Observations: Median What score will she need to earn on the fifth test for the median of her scores to be an 80%? • 79 80 82 70? 75? 79? 80? 81? 82? 83? 84?        

41. Think, Pair, Share • Construct a collection of numbers that has the following properties. If this is not possible, explain why not. mean = 6 median = 4 mode = 4 What is the fewest number of observations needed to accomplish this?

42. Think, Pair, Share • Construct a collection of numbers that has the following properties. If this is not possible, explain why not. mean = 6 median = 6 mode = 4 What is the fewest number of observations needed to accomplish this?

43. Think, Pair, Share • Construct a collection of 5 counting numbers that has the following properties. If this is not possible, explain why not. mean = 5 median = 5 mode = 10 What is the fewest number of observations needed to accomplish this?

44. Think, Pair, Share • Construct a collection of 5 real numbers that has the following properties. If this is not possible, explain why not. mean = 5 median = 5 mode = 10 What is the fewest number of observations needed to accomplish this?

45. Think, Pair, Share • Construct a collection of 4 numbers that has the following properties. If this is not possible, explain why not. mean = 6, mean > mode

46. Think, Pair, Share • Construct a collection of 5 numbers that has the following properties. If this is not possible, explain why not. mean = 6, mean > mode

47. Adding a constant k • Suppose a constant k is added to each value in a data set. How will this affect the measures of center and spread? 5 6 7 9 2 4 1 6 mean = 5 median = 5.5 mode = 6 range = 8

48. Adding a constant k 5 6 7 9 2 4 1 6 5+2= 6+2= 7+2= 9+2= 2+2= 4+2= 1+2= 6+2= 7 8 9 11 4 6 3 8 mean = 5 median = 5.5 mode = 6 range = 8 mean = 7 median = 7.5 mode = 8 range = 8

49. Multiplying by a constant k • Suppose a constant k is multiplied by each value in a data set. How will this affect the measures of center and spread? 5 6 7 9 2 4 1 6 mean = 5 median = 5.5 mode = 6 range = 8

50. Multiplying by a constant k 5 6 7 9 2 4 1 6 5×2= 6×2= 7×2= 9×2= 2×2= 4×2= 1×2= 6×2= 10 12 14 18 4 8 2 12 mean = 5 median = 5.5 mode = 6 range = 8 mean = 10 median = 11 mode = 12 range = 16