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