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, 5. Usea strip of grid paper that has exactly as many boxes as data values. Place each ordered data value into a box. Fold the strip in half. The median is at 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%? A x N = T Jane has 316 points. She needs 400 points. How many more does she need? 84 points

37. 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%?

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? (Note: An “A” is 90% or above) What measure of center are we asking students to consider?

39. 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)

40. 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

41. 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?        

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 = 4 mode = 4 What is the fewest number of observations needed to accomplish this?

43. 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?

44. 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?

45. 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?

46. 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

47. 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

48. 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

49. 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

50. 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