PROJECT: DESCRIPTIVE STATISTICS FOR QUANTITATIVE DATA

Project:  A hybrid vehicle has two types of engines, gas and electric.  Today, they can be purchased in sedan, sport utility vehicle (SUV), or crossover models.

 Objective:  Use Descriptive Statistics to organize raw data into a table, make graphs, find measures of central tendency, dispersion, and outliers.

A sample of hybrid vehicle prices and mileage (city / hwy) produced the following results.

Cadillac Escalade 2WD:  $70,735 20 / 21   Lexus GS450h:  $56,400 22 / 25
Cadillac Escalade 4WD:  $73,285 21 / 21   Lexus GS600:  $105,885 20 / 22
Chevy Malibu:  $24,695 26 / 34   Lexus RS FWD:  $41,600 28 / 32
Chevy Tahoe 2WD:  $50,455 21 / 22   Lexus RS AWD:  $43,250 28 / 30
Chevy Tahoe 4WD:  $53,260 20 / 20   Mazda Tribute 2WD:  $29,175 31 / 34
Chrysler Aspen $44,770 19 / 20   Mazda Tribute 4WD:  $33,145 27 / 29
Dodge Durango: $44,540 19 / 20   Mercury Mariner 4x2:  $29,995 31 / 34
Ford Escape 2WD:  $29,750 31 / 34   Mercury Mariner 4x4:  $31,745 27 / 29
Ford Escape 4WD:  $31,500 27 / 29   Mercury Milan:  $27,500 36 / 41
Ford Fusion:  $27,270 36 / 41   Nissan Altima:  $26,650 33 / 35
GMC Yukon 2WD:  $50,920 21 / 22   Saturn AURA:  $24,930 26 / 34
GMC Yukon 4WD:  $53,730 20 / 20   Saturn VUE:  $26,955 25 / 32
Honda Civic:  $23,550 40 / 45   Toyota Camry:  $26,150 33 / 34
Honda Insight:  $19,800 40 / 43   Toyota Highlander:  $34,700 25 / 27
Lexus HS:  $34,200 34 / 35   Toyota Prius: $22,070 45 / 48

I.  Perform the following operations:
A.  Sort the data in ascending order.

Use the TI-83 or TI-84 to make a rough draft of a frequency histogram.
1.  Press the "STAT" button.
2.  With "EDIT" highlighted select "1:Edit" by pressing "ENTER".

3.  If there is data in List 1 (L1) clear it by using the up arrow to highlight "L1". 
     Then press "CLEAR" and "ENTER".
4.  Enter your data into List 1 (L1) by entering each value and pressing "ENTER"
     after each value.
5.  Press the buttons "2nd" and "MODE" (QUIT) to signify the end of the data.

6.  Press the "STAT" button.
7.  Use the down arrow and select "2:  SortA(" for sort in ascending order and
     press "ENTER".
8. Press "2nd",  "1" and ")" for List 1 and press "ENTER". 

To view the sorted data:
9.  Press the "STAT" button.
10.  With "EDIT" highlighted select "1:Edit" by pressing "ENTER".

B.  Make a table with seven classes.

1.  To use the TI-83 to organize the data
      a.  Press "2nd", "Y = " and "ENTER".  This will take you to the
           "Stat Plots" Menu
      b.  Under "Plots1"
            i.  Highlight "ON" and press "ENTER".
            ii.  Use the arrows to highlight the Bar Graph and press "ENTER".
            iii.  Use the arrows to get to "XList": and  press "2nd" "1". 
                   This refers the calculator to the data stored in List 1.
            iv. Enter "1" at "Freq:" and press "ENTER".

        Determine the class width. 

        

                  

         Choose a value for the class width that is easy to work with and makes the data easy to read.
          Let the class width be $12,500.

         Choose the starting point for the first class. $19,000. 
        Starting at $19,000 and adding on 7 classes of width $12,500 will end at $19,000 + 7 * $12,500 = $106,500.
        Add one more class width for your Xmax.  Xmax = $106,500 + $12,500 = $119,000.  Use your class width as 
         your Xscal.
         Ymin = 0
         Choose a number for Ymax, if it doesn't work, try again.  See the note following step 7
         Yscl = 1

4.  Press "Window" and use the settings on the right.  
    Note:  The settings are based on the values used to construct the table 
     for the data.  "Xmin" is the starting point of the first class.  "Xmax" is the 
     upper value of the last class plus a class width.  "Xscl" is the class width.

5.  Press "GRAPH" to view the frequency histogram of the 30 HYBRID prices.
6.  Press "Trace".  An asterisk will appear on the first bar.  Referring to the
     picture on the right.  This says that 13 data values fall within the first
     class (At least $19,000 but less than $31,500.)
7.  Use the right arrow to get the frequencies of the other classes.

Note:   If the top of any of the bars is not visible, then press "Window" and reset the "Ymax" value to a larger value until the tops of all the bars are visible.

           The table for the data is:

Hybrid Prices
Thousands of Dollars		 Frequency Relative Frequency Class Mark
Thousands of Dollars
19 - 31.5 13 13 / 30 0.43 25.25
31.5 - 44 7 7 / 30 0.23 37.75
44 - 56.5 7 7 / 30 0.23 50.25
56.5 - 69 0 0 62.75
69 - 81.5 2 2 / 30 0.07 75.25
81.5 - 94 0 0 87.75
94 - 106.5 1 1 / 30 0.03 100.25

C.  Use the table in Part II to construct by hand on graph paper:
      1.  Relative frequency polygon.

      2.  Frequency histogram.

D.  Use your calculator to find basic statistics for the data    

 Using the TI-83 to calculate the Mean, Median, First Quartile, Third Quartile and Standard Deviation.
  1. Press the "STAT" button.
  2. Use the right arrow to highlight the "CALC" selection.
  3. Choose "1:1-Var Stats" by pressing "ENTER".
     4.  Press "2nd",  and "1" for List 1 and press "ENTER". 

     5.  Use the down arrow to scroll the remaining statistics on the screen.

        1.  Mean  $39,753.67
        2.  Standard Deviation  $18,755.54
        3.  Median   $32,445.00
        4.  First Quartile  $26,955.00
       5.  Third Quartile  $50,455.00

E.  Use you calculator to construct an IQR Boxplot

Using the TI-83 to calculate an IQR boxplot.
1.  To use the TI-83 to construct an IQR boxplot
      a.  Press "2nd", "Y = " and "ENTER".  This will take you to the
           "Stat Plots" Menu
      b.  Under "Plots1"
            i.  Highlight "ON" and press "ENTER".
            ii.  Use the arrows to highlight the IQR Boxplot and press "ENTER".
            iii.  Use the arrows to get to "XList": and  press "2nd" "1". 
                   This refers the calculator to the data stored in List 1.
            iv. Enter "1" at "Freq:" and press "ENTER".
           v.  Select the mark you want to identify any outlers.

2.  Using the same "Window" settings for the histogram, press "GRAPH"

Note:  The square to the right of the IQR boxplot means that there is at least one value that is an outlier. 

   Use the values from Part C to construct an IQR boxplot.
   IQR = $50,455.00  - $26,955.00 = $23,500.00
   Left Whisker = $26,955 - 1.5($23,500.00) = - $8,295.00               Since the price is negative, use $0.
   Right Whisker = $50,455 + 1.5($23,500.00) = $85,705.00

   Determine which data values, if any, are outliers.  $105,885.00

                The IQR boxplot is:   

Note:  This IQR boxplot agrees with the IQR boxplot generated by the TI 83 / 84 calculator.  However, it is more informative as its lists the values for the parts of the IQR boxplot and outliers.

II.  Using City Mileage as data:
      A.  Sort the data in ascending order.

      B.  Make a table with seven classes.

           Determine the class width. 

              .  Let 4 be the class width.

 

        The table for the data is:

City Mileage Frequency Relative Frequency
19 - 23 10 10 / 30 0.33
23 - 27 4 4 / 30 0.13
27 - 31 5 5 / 30 0.17
31 - 35 6 6 / 30 = 0.20
35 - 39 2 2 / 30 0.07
39 - 43 2 2 / 30 0.07
43 - 47 1 1 / 30 0.03

      C.  Use the table in Part B to construct a relative frequency histogram.
          Note:  You can use software (Excel, MINITAB, etc.) or draw them by hand using graph paper.

      D.  Calculate the:
           1.  mean  27.7        2.  median   27.0

      E.  Which measure of "Average" do you feel best describes the City Mileage for a hybrid vehicle?
              Based on the shape of the graph, not symmetric, not Normal, use the median 27.0.

 

Click on the hand to return to the "It's Real!", Seniors Exclaim  projects.  

Click on the hand to return to the Gen. Ed. Math. projects.