Slide 1

5

AUTOMOBILE OWNERSHIP

5-1 5-2 5-3 5-4 5-5

Classified Ads Buy or Sell a Car Graph Frequency Distributions Automobile Insurance Linear Automobile Depreciation

Financial Algebra © Cengage/South-Western

Slide 2

5

AUTOMOBILE OWNERSHIP

5-6 5-7 5-8 5-9

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 stem and-leaf plots to display information.

Slide 3 Financial Algebra © Cengage/South-Western

Slide 4

Key Terms

from 5-2  mean   outlier ascending order   median range    quartiles lower quartile upper quartile

(from 5-2 & 5-3)

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 Frequency

540 1 550 4 600 675 3 1 700 750 775 800 7 1 2 1 870 900 990 1000 1200 1 2 6 1 3 Total 33 Financial Algebra © Cengage Learning/South-Western

Slide 8

CHECK YOUR UNDERSTANDING

Use the frequency distribution from Example 1 to find the number of car stereos selling for less than $800.

Price Frequency

540 1 550 4 600 675 3 1 700 750 775 800 7 1 2 1 870 900 990 1000 1200 1 2 6 1 3 Total 33 Financial Algebra © Cengage Learning/South-Western

Example 2

Find the mean of the car stereos prices from Example 1.

 Create a 3 rd product of 1 st  column to show 2 columns. Find total of 3 rd column, divide by total prices

Price Frequency

540 1 550 600 4 3 675 700 750 775 1 7 1 2 800 870 900 990 1000 1200 1 1 2 6 1 3 Total 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 Slide 9 Financial Algebra © Cengage Learning/South-Western

Slide 10

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.

Price Frequency

540 1 550 600 4 3 675 700 750 775 1 7 1 2 800 870 900 990 1000 1200 1 1 2 6 1 3 Total 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

6 5 8 7 1 0 4 3 2 540 550 600 675 700 750 775 800 870 900 990 1000 1200 Slide 11

Price Frequency

540 1 550 4 600 675 3 1 700 750 775 800 7 1 2 1 870 900 990 1000 1200 1 2 6 1 3 Total 33 Financial Algebra © Cengage Learning/South-Western

12 10 8 6 4 2 0

Histogram (cont.)

 Group numbers into ranges to make data more meaningful

Frequency

500 600 700 800 900 1000 1100 1200

Price Frequency

500 5 600 700 4 10 800 900 1000 1100 1200 2 8 1 0 3 Slide 12 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 stem- and-leaf plot. What are the mean and the median of this distribution?

Slide 13 Note the key 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 15 th and 16 th positions.

 15 th =39; 16 th = 39  median = 39 Slide 14 Financial Algebra © Cengage Learning/South-Western

Slide 15

CHECK YOUR UNDERSTANDING

Find the range and the upper and lower quartiles. Range: highest – lowest  72 – 11 = 61 Financial Algebra © Cengage Learning/South-Western

Quartiles

divide the data into 4 equal groups.

 Q 2 , the median, creates 2 groups  Q 2 = 39  Q 1 is the lower quartile.  Find the median of the data below Q 2 .

 There are 15 numbers in lower group. Q 1 is in the 8 th position, 23.

 Q 3 is the upper quartile.

 Find the median of the data above Q 2 .

 There are 15 numbers in the upper group. Q 3 position, 55 .

is in the 23 rd Slide 16 Financial Algebra © Cengage Learning/South-Western

EXAMPLE 4

Rod, from Example 3, found another graph called a box- and-whisker plot, or boxplot.

Slide 17 • Plot the minimum, 3 quartiles and maximum on a number line.

• Draw a box using Q 1 and Q 3 at either end.

• Draw a line through Q 2 , the median of all the data.

Find the interquartile range (IQR), Q 3 – Q 1 • 55 – 23 = 32 Financial Algebra © Cengage Learning/South-Western

Slide 18

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? 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

Slide 20

CHECK YOUR UNDERSTANDING

Examine the modified boxplot. Is 400 an outlier? Financial Algebra © Cengage Learning/South-Western