text: ### Financial Algebra - OCPS Teacher Server
  
  ```5
  5-1
  5-2
  5-3
  5-4
  5-5
  Slide 1
  AUTOMOBILE
  OWNERSHIP
  Graph Frequency Distributions
  Automobile Insurance
  Linear Automobile Depreciation
  Financial Algebra
  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
  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
  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
  Why are graphs used so frequently
  in mathematics, and in daily life?
  Can graphs be used to mislead people?
  Slide 5
  Financial Algebra
  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
  Slide 6
  Financial Algebra
  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
  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
  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
  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
  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
  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
  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
  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
  Find the range and the upper and lower quartiles.
  Range: highest – lowest
  72 – 11 = 61
  Slide 15
  Financial Algebra
  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
  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
  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
  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
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