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Graph Frequency Distributions Section 5 - 3 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? Graph Frequency Distributions Today: 1) Create a frequency chart a) Including an interval frequency chart 2) Find the mean from a frequency chart Graph Frequency Distributions You want to purchase a car stereo. You find 33 ads for the stereo you want and arranged them ascending order: What is wrong with using this data? $540 $600 $700 $700 $870 $990 $1,200 $550 $600 $700 $750 $900 $990 $1,200 $550 $600 $700 $775 $900 $990 $1,200 $550 $675 $700 $775 $990 $990 $550 $700 $700 $800 $990 $1,000 $540 $550 $550 How many car stereos $550 $550 $600 are priced below $800? $600 $600 $675 $700 $700 $700 How many car stereos $700 $700 $700 are priced below $600? $700 $750 $775 $775 $800 $870 How many car stereos $900 $900 $990 are priced above $990 $990 $990 $1,000? $990 $990 $1,000 $1,200 $1,200 $1,200 Price P($) $540 $550 $600 $675 $700 $750 $775 $800 $870 $900 $990 $1,000 $1,200 Frequency f Graph Frequency Distributions The following data was collected on the weight of packages shipped by a manufacturing company. 13 49 32 16 56 57 65 26 48 45 68 23 44 27 43 35 35 44 22 15 30 46 43 65 What is the major problem with creating a frequency graph for this data? How can this problem be resolved? 36 62 35 Graph Frequency Distributions 13 44 36 68 43 48 30 16 35 49 27 62 23 65 65 22 56 35 32 43 35 45 46 26 15 57 44 Weight Frequency (f) Graph Frequency Distributions Create an interval frequency distribution chart containing the following data. 14 49 71 26 19 64 74 66 55 22 62 75 47 88 54 44 78 59 39 16 18 22 88 93 71 37 49 35 29 74 Graph Frequency Distributions $ Amount 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 Frequency (f) 3 4 4 8 2 3 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 49 71 26 19 64 74 66 55 22 62 75 47 88 54 44 78 59 39 16 18 22 88 93 71 37 49 35 29 74 Graph Frequency Distributions $ Amount 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 80 - 89 90 - 99 Frequency (f) 4 4 3 4 3 3 6 2 1 Graph Frequency Distributions Finding the mean from a frequency chart: 1) Multiply the price by the frequency • If the chart is an interval chart, use the midpoint of the intervals 2) Find the sum of the products 3) Divide the sum by the total number of tally’s Product P(f) Price P($) Frequency f $540 1 $550 4 $540 $2,200 $600 3 $1,800 $675 1 $700 7 $750 1 $775 2 $675 $4,900 $750 $1,550 $800 1 $870 1 $900 2 $800 $870 $1,800 $990 6 $5,940 $1,000 1 $1,200 3 $1,000 $3,60 2) Find the sum of the products: = $26,425 3) Divide this sum by the number of tally’s $26,425 33 = $800.76 Graph Frequency Distributions How can we multiply the amount by the frequency? $ Amount 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 Frequency 3 4 4 8 2 3 938 Mean = = 39.1 24 Midpt Product 14.5 24.5 43.5 98 34.5 44.5 54.5 64.5 138 356 109 193.5 Graph Frequency Distributions $ Amount 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 70 - 79 80 - 89 90 - 99 Frequency Mid pt 4 14.5 4 24.5 3 34.5 4 44.5 3 54.5 3 64.5 6 74.5 2 84.5 1 94.5 Product 58 98 103.5 178 163.5 193.5 447 169 94.5 Mean = $50.17 Graph Frequency Distributions Section 5 - 3 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 35 68 34 63 61 27 50 58 36 48 39 19 68 27 43 52 35 54 23 42 18 45 47 26 52 19 Graph Frequency Distributions How can we multiply the amount by the frequency? $ Amount 10 – 19 20 – 29 30 – 39 40 – 49 50 – 59 60 – 69 Frequency Midpt 3 14.5 5 24.5 5 34.5 44.5 5 54.5 5 64.5 4 1091.5 = $40.43 Mean = 27 Product 43.5 122.5 172.5 222.5 272.5 258 Graph Frequency Distributions Yesterday: 1) Create a frequency chart a) Including an interval frequency chart 2) Find the mean from a frequency chart Today: 1) Read a stem & leaf plot 2) Graph box & whisker plots Graph Frequency Distributions 1 0 2 2 4 3 8 5 9 7 8 10 15 17 18 22 24 38 39 Graph Frequency Distributions 1 2 3 4 8 0 0 2 9 9 2 3 3 4 4 4 4 6 8 9 9 1 2 4 5 6 7 3 Find the mean, mode, and 4 quartiles from this data: Q1 = 23 Q 2 = 27 Mean = 28 Mode = 24 Q3 = 32.5 Q 4 = 43 Graph Frequency Distributions Steps to creating a box and whisker chart 1) Find the four quartiles 2) Draw a box from 3) Draw a vertical line in the box at 4) Draw whiskers out to your lowest and highest data values Q1 to Q3 Q2 Graph Frequency Distributions Q1 = 23 Q 2 = 27 18 23 Q3 = 32.5 27 32.5 Q 4 = 43 43 Graph Frequency Distributions You are doing research on the number of gasoline price changes per year. You have collected the following data. 1 2 3 4 5 6 7 1 0 8 0 2 3 2 a) Put this data in a box and whisker graph 1 2 3 7 9 3 6 6 8 9 9 9 9 9 2 4 4 4 5 5 5 6 7 b) Are there any outliers? Graph Frequency Distributions Q1 = 23 11 Q 2 = 39 23 Q3 = 55 39 Q 4 = 72 55 IQR: 55 – 23 = 32 Lower Boundary: 23 – (1.5) (32) = -25 Upper Boundary: 55 + (1.5) (32) = 103 72 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 Graph Frequency Distribution Page 236, 2-12