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 3 - Problem 14, page81.

Date: February 16, 2004

Question:
Use the grouped frequency table you constructed for Exercise 15 in Chapter 2 to complete part (a) below:

a.    Calculate the mean, median, and mode for the post-instruction score on the mathematics subtest of the Iowa Test of Educational Development (ited9).

Answer:

Table Copied from Exercise 15:
 

Score Interval

 Cumulative Midpoint
(X)
 		 Frequency
(f)		 Cumulative Frequency
(cf)
96-98 97 3 49
93-95 94 1 46
90-92 91 3 45
87-89 88 3 42
84-86 85 6 39
81-83 82 4 33
78-80 79 6 29
75-77 76 2 23
72-74 73 3 21
69-71 70 3 18
66-68 67 2 15
63-65 64 3 13
60-62 61 5 10
57-59 58 3 5
54-56 55 0 2
51-53 52 1 2
48-50 49 0 1
45-47 46 1 1
interval width
= 3		 X f cf

 

____________________________________________________________________________________________________

The mean for grouped data is found using formula 3.4, text page 74.

Multiply each score times its frequency;
Find the sum of all those products and call it the numerator;
 

Add all the frequencies together and call this the denominator;

The mean for grouped data is the numerator / denominator.

In this problem, the table does not give us the individual scores,
so on the basis of what was given, the Mean for group data cannot be calculated by hand.

________________________________________________________________________________________________________

Formula 3.3 finds the median for grouped data.

The median will lie in the 78-80 interval, because with an odd number of participants (49) the 25th score resides in the interval 78-80.

The lower limit of the j-score is 77.5;

N= 49;  N/2 = 49/2 = 24.5

cf sub j-1 = 23

24.5 - 23 = 1.5

f sub j = 6

1.5/6 = .25

J = score interval  = 3

3 x .25 =.75

77.5 + .75 = 78.25

 78.25 = Median

____________________________________________________________________________________________


The mode for grouped data is the midpoint of the interval with the highest frequency.

This distribution is bimodal since the intervals 78-80 and 84-86 both contain frequencies of 6.

The modes are 79 and 85 respectively.

__________________________________________________________________________________________________________
 

 

Question:
 

b.    Use the SPSS program and SPSS data (math.sav) bank provided with your textbook to find the mean, median, and mode for the post-instruction score on the mathematics subtest of the Iowa Test of Educational Development in part (a).

Answer:

How to do it, step by step:

Load the CD containing data;
Load SPSS;
Double-click SPSS;
File - Open - Math.sav; Press Enter
Analyze Menu - Descriptive Statistics - Descriptives
Scroll to and select ITED Math Score ITED9 ;
Click the move arrow;
Click options; Click Mean

Note found under Descriptives: Related Procedures:
For the median, mode, quartiles, percentiles, and a histogram, use the Frequencies procedure. To compute summary statistics for each of several groups of cases (for example, if you want separate statistics for males and females or for people living in four regions of a country), use the Explore or the Means procedure. You can also use Split File on the Data menu.

Click Continue
Click OK

Mean on ITED9

 

Right-click the picture
Choose Select Object
Select a location in Frontpage
From Edit menu choose Paste command
Save Frontpage.
Refresh the web.

Click Left pointing arrow

Choose Analyze - Descriptives - Frequencies
Select ITED9th Grade Math Scores and arrow it into the Variables Box
Click Statistics
Click Mean, Median, and Mode
Click Continue
Click OK

Right-click the object
Copy
Select a location on Frontpage
Paste
Save
Refresh the web.
Mean, Median, and Mode on ITED9

 

 

 

 

Question:
 

c.    What differences exist in the mean, median, and mode for parts (a) and (b)?  Account for any differences that exist in each measure.
 

Answer:

I can't comment on the mean since I haven't copied a table containing the individual scores.  (I could probably go back into SPSS and find such data on an individual basis.)

The median is 78.25 by hand and 79.00 using SPSS. 

I have a problem with the text:
Formula 3.3 on page 71 for a Grouped Data median is NOT the same as the formula in Table 3-9 for the Grouped Data median. (I think the formula on page 74 is incorrect, because its numerator does not place parenthesis in the same positions given previously in Formula 3.3)

I have one other problem - on page 71, the interval width is reported as 5, for score intervals like 3-7;
In this problem the interval width is 3 for score intervals like 45-47.
So how do you REALLY determine J?

 

The modes are 79 and 85; SPSS reports multiple modes, and shows the lowest in value.  SPSS may be using a different score interval.

 


filename: StatHW2Ch3Prob14page81TomMeyer.doc

Tom Meyer

Thomas Meyer