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AUTOMOBILE OWNERSHIP

5-1 Classified Ads5-2 Buy or Sell a Car5-3 Graph Frequency Distributions5-4 Automobile Insurance5-5 Linear Automobile Depreciation

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AUTOMOBILE OWNERSHIP

5-6 Historical and Exponential Depreciation5-7 Driving Data 5-8 Driving Safety Data5-9 Accident Investigation Data

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5-3GRAPH FREQUENCY DISTRIBUTIONS

Create a frequency distribution from a set of data.

Use box-and-whisker plots and stem-and-leaf plots to display information.

OBJECTIVES

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from 5-2meanoutlierascending ordermedian rangequartiles lower quartileupper quartile

5-2 cont. interquartile range (IQR)mode

from 5-3 frequency distribution stem-and-leaf plot box-and-whisker plot

Key Terms (from 5-2 & 5-3)

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Why are graphs used so frequently in mathematics, and in daily life?

Can graphs be used to mislead people?

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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?

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Example 1 (cont.) Create a frequency distribution.

Add the frequencies to be sure no numbers are left out.

Price Frequency 540 1550 4600 3675 1700 7750 1775 2800 1870 1900 2990 6

1000 11200 3Total 33

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

CHECK YOUR UNDERSTANDINGPrice Frequency 540 1550 4600 3675 1700 7750 1775 2800 1870 1900 2990 6

1000 11200 3Total 33

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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

Price Frequency Total540 1 540550 4 2,200600 3 1,800675 1 675700 7 4,900750 1 750775 2 1,550800 1 800870 1 870900 2 1,800990 6 5,940

1000 1 1,0001200 3 3,600Total 33 26,425

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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.

CHECK YOUR UNDERSTANDINGPrice Frequency Total540 1 540550 4 2,200600 3 1,800675 1 675700 7 4,900750 1 750775 2 1,550800 1 800870 1 870900 2 1,800990 6 5,940

1000 1 1,0001200 3 3,600Total 33 26,425

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HistogramA histogram is a graph of frequencies.Examples: Making HistogramsPut frequencies on vertical axis.Bars should touch.

Price Frequency 540 1550 4600 3675 1700 7750 1775 2800 1870 1900 2990 6

1000 11200 3Total 33

540 550 600 675 700 750 775 800 870 900 990 1000 12000

1

2

3

4

5

6

7

8

Frequency

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Histogram (cont.)Group numbers into ranges to make data more meaningful

Price Frequency500 5

600 4

700 10

800 2

900 8

1000 1

1100 0

1200 3

500 600 700 800 900 1000 1100 12000

2

4

6

8

10

12

Frequency

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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?

EXAMPLE 3

Note the key

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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 = 39median = 39

EXAMPLE 3 (cont.)

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Find the range and the upper and lower quartiles.

Range: highest – lowest72 – 11 = 61

CHECK YOUR UNDERSTANDING

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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.

Quartiles

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Rod, from Example 3, found another graph called a box-and-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

EXAMPLE 4

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Based on the box-and-whisker plot from Example 4, what percent of the gas stations had 55 or fewer price changes?

CHECK YOUR UNDERSTANDING

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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?

EXAMPLE 5

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Examine the modified boxplot. Is 400 an outlier? CHECK YOUR UNDERSTANDING