Concept explainers
For the following set of scores, find the value of each expression:
X |
1 |
2 |
4 |
1 |
3 |
a. ΣX2
b. (ΣX)2
c. Σ(X + 1)
d. Σ(X + 1)2
a.
To Find: The value of
Answer to Problem 19P
Explanation of Solution
Given info:
X represents the scores. The scores are 1, 2, 4, 1, and 3.
Calculation:
X represents the scores.
Y represents the values when square of each score is done, that is:
Then,
Software procedure:
Step-by-step procedure to obtain the
- Go to Variable View> Enter the name of the variable as X and second variable as Y.
- Go to Data View>Enter the values of X.
- Go to Transform>Choose Compute variable>Enter Y in Target Variable> choose X >Move X to Numeric Expression.
- Choose (^) sign > Enter 2.
- Choose OK.
- Choose Analyze > Descriptive Statistics> choose Descriptive.
- Select Y and move it under variable(s)>Choose Options>Select Sum.
- Choose Continue> choose OK.
Output using the SPSS software is given below:
Descriptive Statistics | ||
N | Sum | |
Y | 5 | 31.00 |
Valid N (listwise) | 5 |
From the SPSS output, the value of
Conclusion:
The value of
b.
To Find: The value of
Answer to Problem 19P
Explanation of Solution
Given info:
X represents the scores.
The scores are 1, 2, 4, 1 and 3.
Calculation:
X represents the scores.
Software procedure:
Step-by-step procedure to obtain the
- Go to Variable View> Enter the name of the variable as X.
- Go to Data View>Enter the values of X.
- Choose Analyze > Descriptive Statistics> choose Descriptive.
- Select X and move it under variable(s)>Choose Options>Select Sum.
- Choose Continue.
- choose OK.
Output using the SPSS software is given below:
Descriptive Statistics | ||
N | Sum | |
X | 5 | 11.00 |
Valid N ( list wise ) | 5 |
From the SPSS output, the value of
The value of
Conclusion:
The value of
c.
To Find: The value of
Answer to Problem 19P
Explanation of Solution
Given info:
X represents the scores.
The scores are 1, 2, 4, 1 and 3.
Calculation:
X represents the scores.
Y represents the values when 1 is added from each score, that is:
Then,
Software procedure:
Step-by-step procedure to obtain the
- Go to Variable View> Enter the name of the variable as X and second variable as Y.
- Go to Data View>Enter the values of X.
- Go to Transform>Choose Compute variable>Enter Y in Target Variable
- Choose X >Move X to Numeric Expression.
- Choose (+) sign > Enter 1.
- Choose OK.
- Choose Analyze > Descriptive Statistics> choose Descriptive.
- Select Y and move it under variable(s)>Choose Options>Select Sum.
- Choose Continue
- choose OK.
Output using the SPSS software is given below:
Descriptive Statistics | ||
N | Sum | |
Y | 5 | 16.00 |
Valid N (listwise) | 5 |
From the SPSS output, the value of
Conclusion:
The value of
d.
To Find: The value of
Answer to Problem 19P
Explanation of Solution
Given info:
X represents the scores.
The scores are 1, 2, 4, 1 and 3.
Calculation:
X represents the scores.
Y represents the values when 1 is added from each score and then squaring it that is:
Then,
Software procedure:
Step-by-step procedure to obtain the
- Go to Variable View> Enter the name of the variable as X and second variable as Y.
- Go to Data View>Enter the values of X.
- Go to Transform>Choose Compute variable>Enter Y in Target Variable.
- Write (X+1)*(X+1) in Numeric Expression.
- Choose OK.
- Choose Analyze > Descriptive Statistics> choose Descriptive.
- Select Y and move it under variable(s)>Choose Options>Select Sum.
- Choose Continue> choose OK.
Output using the SPSS software is given below:
Descriptive Statistics | ||
N | Sum | |
Y | 5 | 58.00 |
Valid N (listwise) | 5 |
From the SPSS output, the value of
Conclusion:
The value of
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