Distance Education Statistics
Lab A
Eric Parslow
and
Russell T. Hurlburt
University of Nevada, Las Vegas
This lab will consist of 3 parts:
Familiarization with the algebraic procedures
introduction to ESTAT and its computation program datagen
The quiz
Part I. Familiarization with the algebraic procedures you will be using throughout the course
Below is a series of exercises that you should complete in their entirety.
Perform all the calculations by hand, on paper, using basic calculator functions.
Answers and explanations will be given as you go.
If your answer matches the one given, continue on.
If your answer is different, read the explanation and try the problem again before proceeding.
A quick reminder: the numbers listed in a column below each 'X' and 'Y' are considered data sets/groups. The Greek capital letter Sigma (
) means "sum of:"
1.
X
4
6
8
_____
This problem requires that you take the sum of the three values of X (4, 6, and 8).
1. ANSWER
X
4
6
8
18
Explanation: Add directly down the X column: 4+6+8=18
2.
X
2
3
5
6
_____
Be sure to create new column(s) to show each computation.
2. ANSWER
X
2
3
5
6
0
Explanation: First make a new column with the heading X-4.
The new column will look like this:
X-4
-2
-1
1
2
Then add directly down the new column (-2)+(-1)+1+2=0
3.
X
2
1
3
4
_____
Be sure to create new column(s) to show each computation.
3. ANSWER
X
2
1
3
4
30
Explanation: Make a new column headed X
2
, which looks like this:
X
2
4
1
9
16
Then sum directly down the column: 4+1+9+16=30.
4. Here is the same data as in #3:
X
2
1
3
4
_____
4. ANSWER
X
2
1
3
4
100
Explanation: The correct reading of the problem is:
"the sum of X, that quantity squared."
Therefore, no new columns need to be created.
Sum directly down the X column (2+1+3+4=10).
Then, square that quantity (10*10=100).
NOTE that we found in #3 that
30.
However, in #4 we found that
100.
IT IS ABSOLUTELY ESSENTIAL THAT YOU UNDERSTAND THE FUNCTIONING OF PARENTHESIS AND WHY PROBLEMS 3 AND 4 GIVE DIFFERENT ANSWERS.
5.
X
1
3
4
6
10
_____
5. ANSWER
X
1
3
4
6
10
115.2
Explanation: Read the question as:
"the sum of X, that quantity squared, divided by n
'n' is number of pieces of data in a group or set.
So, calculate the sum of X (1+3+4+6+10=24)
Square that sum (24*24=576).
Divide that amount by the number of pieces of data (576/5=115.2).
6.
X
Y
2
4
3
8
6
2
_____
6. ANSWER
X
Y
2
4
3
8
6
2
1936
Explanation: First make a new column headed XY, like this:
XY
(2*4)
8
(3*8)
24
(6*2)
12
Sum down that column (8+24+12=44)
Square that quantity (44*44=1936)
7.
X
Y
7
6
1
2
9
4
10
5
_____
7. ANSWER
X
Y
7
6
1
2
9
4
10
5
4677.75
Explanation: Two new columns must be made, one for X
2
and one for Y
2
X
2
Y
2
49
36
1
4
81
16
100
25
Those columns must then be individually summed.
The sum of the X squareds is 49+1+81+100=231
The sum of the Y squareds is 36+4+16+25=81
To complete the numerator, multiply the two sums (231*81=18711)
n is the number of values in each column, so n = 4.
Finally, divide the 18711 by 4: (18711/4=4677.75)
8.
X
Y
4
2
2
6
3
8
_____
8. ANSWER
X
Y
4
2
2
6
3
8
37.33
Explanation: Essentially, solve the two sets of brackets individually and then multiply...
The First Set of Brackets:
Make a column labeled X
2
and sum down it: (16+4+9=29)
Sum down the column labeled X (4+2+3=9), square that sum (9*9=81),
and divide that sum by 'n' (81/3=27)
Finally subtract 27 from 29 to complete the left hand bracket bracket (29-27=2)
Repeat these step using Y to complete the second set of brackets
The "Y brackets" should give you 18.667.
Finally multiply the sets of brackets together (2*18.667=37.33)
9.
X
Y
1
2
4
4
7
9
9
12
_____
9. ANSWER
X
Y
1
2
4
4
7
9
9
12
6.87
Explanation: First make a new column labeled XY:
XY
(1*2)
2
(4*4)
16
(7*9)
63
(9*12)
108
Sum that column to complete the first term (2+16+63+108=189)
Sum the X and the Y columns individually and multiply:
Sum X: 1+4+7+9=21
Sum Y: 2+4+9+12=27
Sux X times Sum Y: 21*27=567
Divide that product by 'n' to complete the 2nd term
(567/4=141.75)
Subtract the second term from the first term (189-141.75=47.25)
Finally, take the square root of 47.25 = 6.87
YOU HAVE NOW SEEN THE MOST DIFFICULT ALGEBRA IN THE COURSE.
Part II. An introduction to ESTAT and its computation program datagen
Insert the
Personal Trainer
CD, which should launch
Personal Trainer
.
Locate the ESTAT button, and click on it to begin the program.
Once the ESTAT main menu screen appears, click on "datagen", near the bottom of the button list.
Using the up and down arrows, Tab, and Enter to move the cursor between cells
Enter the following data under "variable 1".
Place only one number in each cell.
After entering all the data, return the cursor to the top cell
(this ensures that the final piece of data is included in the
calculations).
X
4
6
3
7
4. Note that in the window underneath the data area, various numbers have appeared. These are the computations related to the data set you have entered.
5. The Macintosh abbreviations are:
'Sum' = 'Sum of observations'
'SS' = Sum of squared observations
'Xbar' = Sample mean (we'll use that in Chapter 4).
's' = sample standard deviation (we'll use that in Chapter 5).
Next to those headings you should read the column:
20
110
5
1.825741
6. Check these calculations on your hand calculator, so you are absolutely sure what datagen is doing.
7. Enter the data set "X
2
" under "variable 2"
It should consist of: 16, 36, 9, 49
8. Note that the Sum of variable 2 is equal to SS of variable 1.
9. Place your cursor under variable 1
10. Click on "Edit Variable" at right.
11. Click on the circle next to "Square them" and then click
"OK"
12. Note that that automatically creates the squares. Verify for yourself that datagen has done this correctly.
13. The "Generate" button will randomly generate variables for you
based on certain parameters. Place the cursor under variable 4
and click on Generate and experiment.
14. Continue to experiment with these functions and the others at
the right until you feel familiar with their functions and uses.
15. You can find additional instruction by clicking on the "Help"
button on the right side of the window.
Part III. The Quiz
When you have mastered both sections I and II, click Take the Lab Quiz below.
You will need the quiz password, which is
7654321
