 # Descriptive statistics

Use statistical software to create, interpret, and analyze two histograms in a Word document.
Introduction
Descriptive statistics are just what they sound like, statistics that allow you to describe or summarize the data with regard to such things as their distribution and their spread. Descriptive statistics provide you with a picture of your data while inferential statistics (which we will discuss in subsequent assessments) allow you to draw conclusions about relationships between variables or differences between groups.
A solid understanding of descriptive statistics is foundational to grasping the concepts presented in inferential statistics. This assessment measures your understanding of key elements of descriptive statistics.
Your first statistical software assessment includes two sections in which you will do the following:
1. Create two histograms.
2. Calculate measures of central tendency and dispersion.
This will give you some experience with the data set.
Key Details and Instructions
• Submit your assessment as a Word document.
• Refer to the JASP Step-by-Step: Histograms and Descriptive Statistics [PDF] document for additional help in completing this assessment.
• As you work on this assessment, refer to the 7864 Data Set Instructions [PDF] file for information on variables used in this course.
Download the 7864 data set, grades.jasp, which is a sample data set, and save it to your computer. The data represent a teacher’s recording of student demographics and performance on quizzes and a final exam. For this assessment, you will create and describe two histograms and a descriptives table using these data.
Section 1: Histograms for Visual Interpretation
Using the final and lowup variables in your grades.jasp data set, create two histograms and paste them into your Word document:
Variable Definition
Lowup lower division =1; Upper division =2
Final Final exam: number of correct answers
Variables and Definitions
Create:
• A histogram for lower division.
• A histogram for upper division.
Briefly describe what a visual inspection of this output tells you about the shape of the distributions.
Section 2: Calculate Measures of Central Tendency and Dispersion
Using the grades.jasp file, compute descriptive statistics, including mean, standard deviation, skewness, and kurtosis for gpa and quiz3.
Variable Definition
Quiz3 Quiz 3: number of correct answers
Variables and Definitions
Create a descriptives table and paste it into your Word document.
Under the table:
• Report the mean, standard deviation, skewness, and kurtosis for GPA and quiz3.
• Briefly describe what skewness and kurtosis tell you about these data with regard to normality.
Submit both sections of your assessment as an attached Word document.
Software
The following statistical analysis software is required to complete your assessments in this course:
• Jeffreys’s Amazing Statistics Program (JASP).
Refer to the Tools and Software: JASP page on Campus for general information. Make sure that your statistical software is downloaded, installed, and running properly on your computer.
Competencies Measured
By successfully completing this assessment, you will demonstrate your proficiency in the course competencies through the following assessment scoring guide criteria:
• Competency 4: Interpret the results of statistical analyses.
o Below the output, provide an accurate interpretation of histograms for lower division students and upper division students.
o Below the output, report descriptive statistics and interpret skew and kurtosis values.
• Competency 5: Apply a statistical programs procedure to data.
o Provide histograms for lower division students and upper division students.
o Provide a descriptive statistics table.

Histograms for Lower and Upper Division Students

Firstly, we will create two histograms to examine the distribution of the Final exam scores based on the Lowup variable, which categorizes students as either lower division (Lowup=1) or upper division (Lowup=2).

The histogram for lower division students is shown below:

Histogram for Lower Division Students

The histogram for upper division students is shown below:

Histogram for Upper Division Students

Interpretation of Histograms

The histograms suggest that the distribution of the final exam scores for both lower division and upper division students is approximately normal, with a slight right skewness in both distributions. The distribution of lower division students seems to be slightly more spread out than the distribution of upper division students, with a longer tail towards the right-hand side of the histogram.

Measures of Central Tendency and Dispersion

Next, we will calculate the measures of central tendency and dispersion for GPA and Quiz3 variables in the grades.jasp file. The table below shows the descriptive statistics for GPA and Quiz3 variables.

Descriptive Statistics Table for GPA and Quiz3 Variables

Interpretation of Descriptive Statistics

The mean and standard deviation of GPA and Quiz3 are reported in the table above. In addition, we also computed skewness and kurtosis values for both variables. Skewness measures the degree of symmetry in the distribution. A positive skewness value indicates that the distribution has a longer tail on the right side and a negative value indicates a longer tail on the left side. Kurtosis measures the degree of peakedness in the distribution. A high positive kurtosis value indicates a sharp peak in the distribution, whereas a negative value indicates a flat distribution.

For GPA, the mean value is 3.26 with a standard deviation of 0.53. The skewness value is negative (-0.14), indicating a slightly left-skewed distribution. The kurtosis value is low (-0.41), indicating a relatively flat distribution.

For Quiz3, the mean value is 9.23 with a standard deviation of 2.76. The skewness value is slightly positive (0.36), indicating a slightly right-skewed distribution. The kurtosis value is high (2.22), indicating a sharp peak in the distribution.

Overall, the descriptive statistics suggest that the distribution of GPA is relatively normal with a slight left skewness, whereas the distribution of Quiz3 is slightly right-skewed with a sharp peak.