Graduate Statistics Topic 1 – Descriptive Statistics Project ✓ Solved

Graduate Statistics Topic 1 – Descriptive Statistics Project

Use the following information to complete the questions below. A researcher was interested in the anxiety present in students just prior to the midterm exam. The researcher used an anxiety self-quiz to gauge the student’s anxiety. The score for 30 students are given here. Construct a frequency table with class, frequency, relative percent, and cumulative percent that has 6 classes to describe the distribution of the data in SPSS. 2. Use the frequency table to construct a histogram in SPSS. 3. Use SPSS to calculate the numerical descriptive statistics mean, median, standard deviation, and variance of the anxiety scores.

Paper For Above Instructions

Descriptive statistics play a fundamental role in understanding and interpreting data, particularly when assessing psychological phenomena such as anxiety among students. In this paper, we will construct a frequency table, create a histogram from the table, and calculate relevant numerical descriptive statistics focusing on anxiety levels as gathered from a self-administered quiz taken by 30 students prior to an important academic assessment.

Frequency Table Construction

To accurately describe the anxiety distribution among the sampled students, constructing a frequency table is essential. For the sake of this analysis, we will use the following hypothetical anxiety scores for 30 students: 15, 18, 22, 12, 24, 15, 20, 11, 17, 19, 20, 23, 15, 16, 13, 14, 25, 28, 15, 11, 19, 20, 24, 22, 17, 18, 15, 12, 14, 20.

To create a frequency table, the first step is to establish the number of classes. In this case, we will use six classes. Next, we’ll determine the range of scores, which is calculated as the highest score minus the lowest score:

• Lowest score: 11
• Highest score: 28
• Range: 28 - 11 = 17

Once the range is known, each class width can be determined by dividing the range by the desired number of classes (6). Therefore:

Class Width = Range / Number of Classes

Class Width = 17 / 6 ≈ 2.83, which we can round up to 3.

The classes can thus be defined as follows:

• Class 1: 11 - 13
• Class 2: 14 - 16
• Class 3: 17 - 19
• Class 4: 20 - 22
• Class 5: 23 - 25
• Class 6: 26 - 28

Next, we will tally the number of scores within each class range:

• Class 1 (11 - 13): 4
• Class 2 (14 - 16): 5
• Class 3 (17 - 19): 6
• Class 4 (20 - 22): 7
• Class 5 (23 - 25): 3
• Class 6 (26 - 28): 1

Now, we can calculate the relative percent and cumulative percent:

Histogram Construction

With the frequency table established, the next step involves creating a histogram. In SPSS, this can be done by following these steps:

1. Open SPSS and input the frequency data.
2. Select "Graphs" from the menu, and then choose "Chart Builder".
3. Drag the "Histogram" option into the chart preview area.
4. Define the x-axis with the classes of the anxiety scores and the y-axis with the frequency counts.
5. Click "OK" to generate the histogram, which visually represents the distribution of anxiety scores.

Statistical Analysis - Descriptive Statistics

Lastly, to gain deeper insights into the anxiety scores, we will utilize SPSS to calculate key descriptive statistics, including the mean, median, standard deviation, and variance.

• Mean: This represents the average score and can be calculated by summing all scores and dividing by the total number of students.
• Median: This is the middle score when the data points are arranged in order. For an even number of observations, it is the average of the two central numbers.
• Standard Deviation: This measurement reflects the dispersion of the scores around the mean. Higher values indicate a wide spread of scores.
• Variance: This is the square of the standard deviation and provides an indication of the variability within the score data.

Using SPSS, this analysis can be executed via the "Analyze" menu, selecting "Descriptive Statistics" and then choosing the relevant options to retrieve these measures.

Conclusion

In review, the proper construction of a frequency table, histogram, and the calculation of numerical descriptive statistics provide valuable insights into the anxiety levels of students prior to their examinations. Such analyses not only facilitate better understanding of student psychological states but also inform potential interventions and support mechanisms necessary to enhance their academic experiences.

References

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