To:  sbaker@odu.edu

From:  Thomas Meyer
tmeyer@ph.vccs.edu
276 656-0283
Patrick Henry Community College

Subject:  Statistics - w/  Dr.Spencer Baker - Homework Assignment #2, Ch 4 - Problem 20, page113.

Date: February 18, 2004

Question:
Use the SPSS program and SPSS data (math.sav) bank to complete the following:

a.    Find the interquartile range, range, standard deviation, variance, skewness, kurtosis, and quartiles for each of the variables that follow:  middle school grade point average (msgpa), middle school mathematics grade point average (mathgpa), pre-instruction attitude toward mathematics (preatt), post-instruction attitude toward mathematics (postatt), pre-instruction score on a novel algebra problem solving test (preprbso), post-instruction score on a novel algebra problem solving test (postpbso), pre-instruction score on a general problem solving test (pregenps), post-instruction score on a general problem solving test (postgnps), pre-instruction score on the mathematics subtest of the Iowa Test of Educational Development *ited*), post-instruction score on the mathematics subtest of the Iowa Test of Educational Development (ited9), and grade point average in algebra for the academic year (algpa).

Answer:

How to do it, step by step:

General Algorithm:
 Step 1:  Get data
Step 2:  Manipulate data
Step 3:  Print out or save data

Step 1 - Get Data
Load the CD containing data;
Load SPSS;
Double-click SPSS;
File - Open - Math.sav; Press Enter

Step 2:  Manipulate data
2A - Get the interquartile range, range, standard deviation, variance, skewness, kurtosis, and quartiles for each of the variables that follow:

1. middle school grade point average (msgpa),
2. middle school mathematics grade point average (mathgpa),
3. pre-instruction attitude toward mathematics (preatt),
4. post-instruction attitude toward mathematics (postatt),
5. pre-instruction score on a novel algebra problem solving test (preprbso),
6. post-instruction score on a novel algebra problem solving test (postpbso),
7. pre-instruction score on a general problem solving test (pregenps),
8. post-instruction score on a general problem solving test (postgnps),
9. pre-instruction score on the mathematics subtest of the Iowa Test of Educational
    Development *ited*),
10. post-instruction score on the mathematics subtest of the Iowa Test of Educational
      Development (ited9), and
11. grade point average in algebra for the academic year (algpa).


Choose Analyze - Descriptive Statistics - Frequencies
Select MSGPA (variable #1) through algpa (variable #11)   and arrow it into the Variables Box
Click Statistics
Click range, standard deviation, variance, skewness, kurtosis, and quartiles
Click Continue
Click OK
Compute the interquartile range for each green variable by hand as "Third quartile - First quartile."
Note the Note below.

 Step 3:  Print out or save data
Right-click the object
Copy the object
Select a location on Frontpage
Paste
Save
Refresh the web.

Here's the answer:

(Note: Unless you tell the computer that the data are interval midpoints, the computer will define the quartiles as the scores earned by the .25Nth and .75Nth persons - text page 89).

 

 

 

1. MSGPA

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 3.49 - 2.66 = 0.83

 

2. MATHGPA

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 3.30 - 2.54 = 0.76


 3. PREATT

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 67.50 - 38.50 = 29.00

4. POSTATT

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 60.00 - 33.50 = 26.50

5. PREPRBSO

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 3.00 - 2.00 = 1.00

6. POSTPBSO

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 6.00 - 3.00 = 3.00

7. PREGENPS

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 2.00 - 1.00 = 1.00

8. POSTGNPS

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 2.00 - 1.00 = 1.00

9. ITED

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 83.00 - 62.00 = 21.00

10. ITED9

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 85.50 - 65.00 = 20.50

 

11. ALGPA

 

The Interquartile range = 3rd Quartile - 1st Quartile  or 3.3300 - 2.3300 = 1.0000

 

 

Question:
 

b.    Using the index of skewness and the index of kurtosis, describe the characteristics of the distribution of scores for each variable.

Answer:

Symmetric distributions can be perceived as flat (platykurtic, tall and high in the middle (leptokurtic) or somewhat in between and having a bell shape (mesokurtic)>

A kurtosis of K = 0 is that assigned to a normal bell shaped distribution.
A negative number for K indicates  a flat or platykurtic distribution;
A positive number for K indicates a leptokurtic or highly peaked distribution.

Larger deviations from zero  indicate more extreme kurtosis.

(text - page 107)

1. MSGPA  : Kurtosis =  .668   ; a higher peak than a normal distribution

 

2. MATHGPA  : Kurtosis = .668   ; a higher peak than a normal distribution   

3. PREATT  : Kurtosis =  .668   ; a higher peak than a normal distribution  

4. POSTATT  : Kurtosis =  .668   ; a higher peak than a normal distribution  

5. PREPRBSO  : Kurtosis =   .668   ; a higher peak than a normal distribution 

6. POSTPBSO  : Kurtosis =  .668   ; a higher peak than a normal distribution  

7. PREGENPS  : Kurtosis =  .668   ; a higher peak than a normal distribution  

8. POSTGNPS  : Kurtosis =  .668   ; a higher peak than a normal distribution  

9. ITED  : Kurtosis = .668   ; a higher peak than a normal distribution   

10. ITED9  : Kurtosis = .668   ; a higher peak than a normal distribution   

11. ALGPA  : Kurtosis =  .668   ; a higher peak than a normal distribution  

 


filename: StatHW2Ch4Prob20page113TomMeyer.doc

Tom Meyer

Thomas Meyer