Graph Frequency Distributions

1. Graph Frequency Distributions Section 5 - 3

2. Graph Frequency Distributions • Why are graphs so important in math? • What would happen if we surveyed everyone in the school about the price of their car? • What would the data look like? • Would it be easy to understand?

3. Graph Frequency Distributions • Today: • Create a frequency chart • Including an interval frequency chart • Find the mean from a frequency chart

4. Graph Frequency Distributions • You want to purchase a car stereo. You find 33 ads for the stereo you want and arranged them ascending order: $540 $550 $550 $550 $550 $600 $600 $600 $675 $700 $700 $700 $700 $700 $700 $700 $750 $775 $775 $800 $870 $900 $900 $990 $990 $990 $990 $990 $990 $1,000 $1,200 $1,200 $1,200 What is wrong with using this data?

5. How many car stereos are priced below $800? $540 $550 $550 $550 $550 $600 $600 $600 $675 $700 $700 $700 $700 $700 $700 $700 $750 $775 $775 $800 $870 $900 $900 $990 $990 $990 $990 $990 $990 $1,000 $1,200 $1,200 $1,200 How many car stereos are priced below $600? How many car stereos are priced above $1,000?

6. Graph Frequency Distributions • The following data was collected on the weight of packages shipped by a manufacturing company. 13 16 65 45 44 35 22 46 36 49 56 26 68 27 35 15 43 62 32 57 48 23 43 44 30 65 35 What is the major problem with creating a frequency graph for this data? How can this problem be resolved?

7. Graph Frequency Distributions 13 16 65 45 44 35 22 46 36 49 56 26 68 27 35 15 43 62 32 57 48 23 43 44 30 65 35

8. Graph Frequency Distributions • Create an interval frequency distribution chart containing the following data. 14 19 55 47 44 39 22 71 35 49 64 22 88 78 16 88 37 29 71 74 62 54 59 18 93 49 74 26 66 75

9. Graph Frequency Distributions

10. Graph Frequency Distributions • You are the manager of The Dress Code Boutique. From the following data representing the dollar sales of each transaction today, construct a frequency distribution using classes with an interval of $10. 14 19 55 47 44 39 22 71 35 49 64 22 88 78 16 88 37 29 71 74 62 54 59 18 93 49 74 26 66 75

11. Graph Frequency Distributions

12. Graph Frequency Distributions • Finding the mean from a frequency chart: • Multiply the price by the frequency • If the chart is an interval chart, use the midpoint of the intervals • Find the sum of the products • Divide the sum by the total number of tally’s

13. 2) Find the sum of the products: $540 = $26,425 $2,200 $1,800 3) Divide this sum by the number of tally’s $675 $4,900 $750 $1,550 $26,425 $800 = $800.76 33 $870 $1,800 $5,940 $1,000 $3,60

14. Graph Frequency Distributions How can we multiply the amount by the frequency? 14.5 43.5 24.5 98 34.5 138 44.5 356 54.5 109 64.5 193.5 938 Mean = = 39.1 24

15. Graph Frequency Distributions Mean = $50.17

16. Graph Frequency Distributions Section 5 - 3

17. Graph Frequency Distributions • Below are prices you have found for different tints for your car. Put them in an interval frequency chart and find the mean price. 25 34 27 36 19 43 54 18 26 35 63 50 48 68 52 23 45 52 68 61 58 39 27 35 42 47 19

18. Graph Frequency Distributions How can we multiply the amount by the frequency? 14.5 43.5 24.5 122.5 34.5 172.5 44.5 222.5 54.5 272.5 64.5 258 1091.5 = $40.43 Mean = 27

19. Graph Frequency Distributions • Yesterday: • Create a frequency chart • Including an interval frequency chart • Find the mean from a frequency chart Today: • Read a stem & leaf plot • Graph box & whisker plots

20. Graph Frequency Distributions 10 15 17 18 1 2 3 0 5 7 8 4 8 9 22 24 38 39

21. Graph Frequency Distributions 1 8 9 9 2 0 2 3 3 4 4 4 4 6 8 9 9 3 0 1 2 4 5 6 7 4 2 3 Find the mean, mode, and 4 quartiles from this data: Mean = 28 = 23 = 27 Mode = 24 = 32.5 = 43

22. Graph Frequency Distributions • Steps to creating a box and whisker chart • Find the four quartiles • Draw a box from to • Draw a vertical line in the box at • Draw whiskers out to your lowest and highest data values

23. Graph Frequency Distributions = 32.5 = 43 = 23 = 27 32.5 18 23 27 43

24. Graph Frequency Distributions • You are doing research on the number of gasoline price changes per year. You have collected the following data. a) Put this data in a box and whisker graph 1 1 1 2 3 7 9 2 0 3 6 6 3 8 8 9 9 9 9 9 0 5 2 2 4 5 5 5 6 7 6 3 4 4 7 2 b) Are there any outliers?

25. Graph Frequency Distributions = 55 = 72 = 23 = 39 55 11 23 39 72 IQR: 55 – 23 = 32 Lower Boundary: 23 – (1.5) (32) = -25 Upper Boundary: 55+ (1.5) (32) = 103

26. Graph Frequency Distributions $3,000 $5,200 $7,000 $9,100 $15,000 What is the IQR? $9,100 - $5,200 = $3,900 Lower Boundary: $5,200 – (1.5)(3,900) = - $650 Upper Boundary: $9,100 + (1.5)(3,900) = $14,950

27. Graph Frequency Distribution • Page 236, 2-12