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5 5-1 5-2 5-3 5-4 5-5 Slide 1 AUTOMOBILE OWNERSHIP Classified Ads Buy or Sell a Car Graph Frequency Distributions Automobile Insurance Linear Automobile Depreciation Financial Algebra © Cengage/South-Western 5 5-6 5-7 5-8 5-9 Slide 2 AUTOMOBILE OWNERSHIP Historical and Exponential Depreciation Driving Data Driving Safety Data Accident Investigation Data Financial Algebra © Cengage/South-Western 5-3 GRAPH FREQUENCY DISTRIBUTIONS OBJECTIVES Create a frequency distribution from a set of data. Use box-and-whisker plots and stemand-leaf plots to display information. Slide 3 Financial Algebra © Cengage/South-Western Key Terms (from 5-2 & 5-3) from 5-2 mean outlier ascending order median range quartiles lower quartile upper quartile Slide 4 5-2 cont. interquartile range (IQR) mode from 5-3 frequency distribution stem-and-leaf plot box-and-whisker plot Financial Algebra © Cengage Learning/South-Western Why are graphs used so frequently in mathematics, and in daily life? Can graphs be used to mislead people? Slide 5 Financial Algebra © Cengage Learning/South-Western Example 1 Jerry wants to purchase a car stereo. He found 33 ads for the stereo he wants and arranged the prices in 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 He is analyzing the prices, but having trouble because there are so many numbers. How can he organize his prices in a helpful format? Slide 6 Financial Algebra © Cengage Learning/South-Western Example 1 (cont.) Create a frequency distribution. Add the frequencies to be sure no numbers are left out. Slide 7 Price 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Total Frequency 1 4 3 1 7 1 2 1 1 2 6 1 3 33 Financial Algebra © Cengage Learning/South-Western CHECK YOUR UNDERSTANDING Use the frequency distribution from Example 1 to find the number of car stereos selling for less than $800. Slide 8 Price 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Total Frequency 1 4 3 1 7 1 2 1 1 2 6 1 3 33 Financial Algebra © Cengage Learning/South-Western Example 2 Find the mean of the car stereos prices from Example 1. Create a 3rd column to show product of 1st 2 columns. Find total of 3rd column, divide by total prices Slide 9 Price 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Total Frequency 1 4 3 1 7 1 2 1 1 2 6 1 3 33 Total 540 2,200 1,800 675 4,900 750 1,550 800 870 1,800 5,940 1,000 3,600 26,425 Financial Algebra © Cengage Learning/South-Western CHECK YOUR UNDERSTANDING Jerry, from Example 1, decides he is not interested in any of the car stereos priced below $650 because they are in poor condition and need too much work. Find the mean of the data set that remains after those prices are removed. Slide 10 Price 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Total Frequency 1 4 3 1 7 1 2 1 1 2 6 1 3 33 Total 540 2,200 1,800 675 4,900 750 1,550 800 870 1,800 5,940 1,000 3,600 26,425 Financial Algebra © Cengage Learning/South-Western Histogram A histogram is a graph of frequencies. Examples: Making Histograms Put frequencies on vertical axis. Bars should touch. Frequency 8 7 6 5 4 3 2 Price 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Total Frequency 1 4 3 1 7 1 2 1 1 2 6 1 3 33 1 0 540 Slide 11 550 600 675 700 750 775 800 870 900 990 1000 1200 Financial Algebra © Cengage Learning/South-Western Histogram (cont.) Group numbers into ranges to make data more meaningful Price Frequency 500 5 600 4 12 700 10 10 800 2 8 900 8 1000 1 1100 0 1200 3 Frequency 6 4 2 0 500 Slide 12 600 700 800 900 1000 1100 1200 Financial Algebra © Cengage Learning/South-Western EXAMPLE 3 Rod was doing Internet research on the number of gasoline price changes per year in gas stations in his county. He found the following graph, called a stemand-leaf plot. What are the mean and the median of this distribution? Note the key Slide 13 Financial Algebra © Cengage Learning/South-Western EXAMPLE 3 (cont.) The mean: Add the data and divide by the frequency (the number of leaves). 1,188 ÷ 30 39.6 The median: The frequency is 30. Since it is even, find the mean of the 15th and 16th positions. 15th =39; 16th = 39 median = 39 Slide 14 Financial Algebra © Cengage Learning/South-Western CHECK YOUR UNDERSTANDING Find the range and the upper and lower quartiles. Range: highest – lowest 72 – 11 = 61 Slide 15 Financial Algebra © Cengage Learning/South-Western Quartiles divide the data into 4 equal groups. Q2, the median, creates 2 groups Q2 = 39 Q1 is the lower quartile. Find the median of the data below Q2. There are 15 numbers in lower group. Q1 is in the 8th position, 23. Q3 is the upper quartile. Find the median of the data above Q2. There are 15 numbers in the upper group. Q3 is in the 23rd position, 55. Slide 16 Financial Algebra © Cengage Learning/South-Western EXAMPLE 4 Rod, from Example 3, found another graph called a boxand-whisker plot, or boxplot. •Plot the minimum, 3 quartiles and maximum on a number line. •Draw a box using Q1 and Q3 at either end. •Draw a line through Q2, the median of all the data. Find the interquartile range (IQR), Q3 – Q1 •55 – 23 = 32 Slide 17 Financial Algebra © Cengage Learning/South-Western CHECK YOUR UNDERSTANDING Based on the box-and-whisker plot from Example 4, what percent of the gas stations had 55 or fewer price changes? Slide 18 Financial Algebra © Cengage Learning/South-Western EXAMPLE 5 The following box-and-whisker plot gives the purchase prices of the cars of 114 seniors at West High School. Are any of the car prices outliers? Slide 19 Financial Algebra © Cengage Learning/South-Western CHECK YOUR UNDERSTANDING Examine the modified boxplot. Is 400 an outlier? Slide 20 Financial Algebra © Cengage Learning/South-Western