G12 graders - Graphing Distributions (Quantitative).pptx

G12 graders - Graphing Distributions (Quantitative).pptx

1. Graphing Distributions Objectives: 1. Graph and Interpret quantitative data.

2. Quantitative Data Seven different ways to display quantitative data: Frequency Distribution Bar Graph Histograms Dot Plots Stem and Leaf Box and Whisker Plots Line Graphs

3. Example 1: The manager of Hudson Auto would like to gain a better understanding of the cost of parts used in the engine tune-ups performed in the shop. She examines 50 customer invoices for tune-ups. 82 82 86 82 98 60 94 93 99 65 53 91 51 100 52 85 96 78 88 71 94 55 85 69 60 62 68 96 89 58 89 82 97 76 62 85 56 90 97 85 91 86 69 84 90 59 68 76 58 92

4. Frequency Distribution: Part Cost ($) Frequency 50-59 8 60-69 9 70-79 4 80-89 14 90-99 14 100+ 1 Total 50

5. Relative Frequency Distribution: Insights: Only 16% of the parts costs are in the $50-59 class. 34% of the parts costs are under $70. The greatest percentage (28%) of the parts costs are in the $80-99 and the $90-99 classes. 2% of the parts costs are $100 or more. Parts Cost ($) Frequency Percent Frequency (%) 50-59 8 16% 60-69 9 18% 70-79 4 8% 80-89 14 28% 90-99 14 28% 100+ 1 2% Total 50 100

6. Histogram: The variable of interest is placed on the horizontal axis. A rectangle is drawn above each interval with its height corresponding to the interval’s frequency , relative frequency , or percent frequency . Unlike a bar graph, a histogram has no natural separation between rectangles of adjacent classes.

7. 28 students How many students scored an A? How many students failed? What percentage of students scored B and C? 6 students 1 student 4 + 12 = 16 students x 100 = 57%   Example 2:

8. How many teenagers listen to their CD players for at least 4 hours each day? 18 teenagers 6 + 2 + 1 = 9 teenagers Example 3:

9. Example 4:

10. Alternatives to Histogram Dot Plot A horizontal axis shows the range of data values. Then each data value is represented by a dot placed above the axis. Stem-and-leaf Plot Similar to a histogram, but it has the advantage of showing the actual data values. The leading digits of each data item are arranged to the left of a vertical line. To the right of the vertical line we record the last digit for each item in rank order. Each line (row) in the display is referred to as a stem . Each digit on a stem is a leaf .

11. Constructing a Dot Plot In an airline training program, the students are given a test in which they are given a set of tasks and the time it takes them to complete the tasks is measured. The following is a list of the time (in seconds) for a group of new trainees. 61, 61, 64, 67, 70, 71, 71, 71, 72, 73, 74, 74, 75, 77, 79, 80, 81, 81, 83 Display the data in a dot plot. Example 5:

12. *A health camp was conducted in a school for children who age between 8 and 10 years old. The wight (in pounds) for 25 students was recorded. Construct a dot plot to represent the data. 68 65 63 63 62 64 65 61 65 61 64 66 64 61 64 65 68 61 62 67 65 63 62 67 66

13. Example 6: The dot plot below shows the height (in inches) of a group of students. For the following statements, state whether they are true, false or unknown. a) T he shortest student was 58 inches tall. b) T he tallest student was a male. c) Half of the students are at least 64 inches tall. d) 80% of the students are shorter than 67 inches. False Unknown False True

14. Example 7: The students in one Math class were asked how many siblings each of them have. The dot plot here shows the results. How many students are in the Math class? How many students have 6 siblings? How many students are the only child? Most of the students have …....... siblings. Answers: 20 students 1 student 3 students 3

15. Constructing a stem and leaf Plot Example 8:

16. *Construct a stem and leaf plot for the following data sets.

17. Example 9: The stem-and-leaf plot shows student test scores. How many students took the test? How many students scored less than 80 points? How many students scored at least 90 points? Answers: 18 students 5 students 4 students

18. Example 10: The stem and leaf plot below represents the amount of practice problems that Jill has completed each day to study for an upcoming test. a) How many days did Jill spend to study for her test? b) On how many days did Jill complete less than 20 problems? 12 days 9 days Stem Leaf 1, 2, 3, 5, 8 1 4, 5, 7, 9 2 1, 3, 7

19. Box and Whisker Plot: https://www.youtube.com/watch?v=fJZv9YeQ-qQ&t=159s&ab_channel=MashupMath Example: Draw a box and whisker plot for the data set: 12, 14, 14, 12, 16, 13, 11, 14, 18

20. Data: 12, 14, 14, 12, 16, 13, 11, 14, 18 Median 14 Minimum 11 Maximum 18 Lower Quartile (Q1) 12 Upper Quartile (Q3) 15 Interquartile Range (IQR) 3

21. Quartiles and Percentiles: The common measures of location are quartiles and percentiles. Quartiles are special percentiles. The first quartile, Q1, is the same as the 25th percentile, and the third quartile, Q3, is the same as the 75th percentile. The median, M, is called both the second quartile and the 50th percentile.

22. *Construct a boxplot for the following data: 3, 7, 8, 8, 5, 9, 10, 12, 14, 7, 1, 3, 8, 16, 8, 6, 9, 10, 13, 7 5-number summary: Minimum: Lower Quartile (Q1): Median (Q2): Upper Quartile (Q3): Maximum: Interquartile Range:

23. *Construct a boxplot for the following data: 42, 58, 67, 55, 40, 69, 66, 51, 46, 48, 68 5-number summary: Minimum: Lower Quartile (Q1): Median (Q2): Upper Quartile (Q3): Maximum: Interquartile Range:

24. 102 75% 88 25% No, since 75% of the students scored above 72.

25. 25% 40 min. Can’t tell 25%

26. What was the: *highest mark *lowest mark scored? What was the median test score for this class? What percentage of students scored 60 or more for the test? What was the interquartile range for this test? The top 25% of students scored a mark between ..... and ..... If you scored 70 for this test, would you be in the top 50% of students in this class? Example 7:

27. Answers: H ighest score: 99 Lowest score: 30 M edian: 73 P ercentage of students scored 60 or more: 75% I nterquartile range: 82 – 60 = 22 T op 25% of students scored between: 82 and 99 No

28. Example 8: Line Graph How many books were sold in weeks 2 and 8? In which week(s) did the store sell 90 books? 120 + 10 = 130 books Weeks 4, 5 and 7

29. Data Distribution Normal Distribution Right Skewed Left Skewed mode = median = mean mode < median < mean mode > median > mean The normal distribution is symmetric and has a central peak where most observations occur. Both halves contain equal numbers of observations. Unusual values are equally likely in both tails. Right skewed distributions occur when the long tail is on the right side of the distribution. Statisticians also refer to them as positively skewed. Left skewed distributions occur when the long tail is on the left side of the distribution.  Statisticians  also refer to them as negatively skewed.

30. Types of Distributions

31. Practice: Describe the distribution of the following graphs: Skewed to the right

32. Practice: Describe the distribution of the following graphs: Skewed to the right

33. Practice: Describe the distribution of the following graphs: Normal distribution

34. Practice: Describe the distribution of the following graphs: Skewed to the left