Statistics week 2 discussion post

Your work on the new student committee was a huge success! The director of new student recruitment has requested that you continue your work on the committee. Specifically, the director would like you to distribute a small survey to the students who attended the weekend event, gauging their level of interest in studying at UMGC. The director is interested in obtaining demographic information from the prospective students, the academic program into which they would enroll, and their overall level of interest in attending UMGC. The survey questions and results are below:

Survey questions given to prospective students

• What is your age?
• Would you live in on-campus housing or off-campus housing?
• Into which academic program would you enroll?
• How likely are you to attend UMGC in the next year? (Rate: 14, 1 is not likely and 4 is very likely)

Your first task is to define the data resulting from each survey question as qualitative or quantitative. If the variable is qualitative, indicate if it is nominal or ordinal. If it is quantitative, indicate whether it is discrete or continuous and whether it is interval or ratio (see graphic below).

Next, create a table (a frequency distribution, stem and leaf plot, or a grouped frequency distribution) to organize the data from one of the variables. Include the table in your post. Does including the relative frequency or cumulative frequency make the table more meaningful? Why do you feel this table best organizes the data?

Then, consider how you might visually display the results as a graph (bar graph, Pareto chart, dot plot, line graph, histogram, pie chart, or box plot). Include the graph in your post. Why did you choose this graph? Explain why you believe this graph is the best choice to display the data.

Finally, find the mean, median, and mode for one of the variables. Which of these measures of central tendency do you think is the best choice for “average” and why? Find the range and standard deviation (measures of dispersion) for the variable. What would a narrower or wider deviation signify in the context of this data?

Please respond to two peers below as well

Fabian –

The survey collected from prospective students includes a mix of qualitative and quantitative data. The variable age is quantitative because it is measured numerically. It is a continuous variable and is measured on a ratio scale, since age has a true zero and meaningful differences between values. Housing choice is qualitative and nominal, as the categories have no order. Academic program is also qualitative and nominal, since each program represents a category without ranking. The variable likelihood to attend UMGC is quantitative but discrete, as it consists of whole numbers from 1 to 4. It is measured on an ordinal scale because the values represent increasing levels of likelihood, but the intervals between them are not guaranteed to be equal.

To organize the data, I created a frequency distribution table for the variable likelihood to attend UMGC, since this variable directly relates to student interest and recruitment goals.

Including relative frequency makes the table more meaningful because it shows the proportion of students at each interest level rather than just raw counts. This helps the director quickly see that the largest groups of students are either very likely or moderately unlikely to attend UMGC. A frequency table is the best way to organize this data because it is simple, clear, and directly compares levels of interest.

To visually display the results, a bar graph would be the best choice for the likelihood variable. A bar graph clearly shows how many students fall into each category and makes comparisons easy at a glance. Since likelihood ratings are discrete and ordinal, a bar graph is more appropriate than a histogram or line graph. A pie chart could also work, but a bar graph better emphasizes differences between categories, which is important for recruitment analysis.

Using the likelihood ratings, the mean is calculated by dividing the total sum of ratings (40) by the number of students (14), resulting in a mean of approximately 2.86. The median is 3, since it is the middle value when the data is ordered. The mode is 2 and 4, making the distribution bimodal. In this case, the median is the best measure of central tendency because the data is ordinal, and the median accurately represents the central position without being affected by how the numbers are spaced.

The range is 3, showing the spread between the lowest and highest likelihood ratings. The standard deviation is approximately 1.07, which indicates a moderate spread in student interest. A narrower deviation would suggest that students feel similarly about attending UMGC, while a wider deviation would indicate more disagreement or uncertainty among prospective students. In this context, the moderate spread suggests mixed but promising interest levels, which could help guide future recruitment strategies.

Erica-

Age: Quantitative, Continuous, Ratio

Housing: Qualitative, Nominal

Program: Qualitative, Nominal

Likely to attend: Quantitative, Discrete, Interval

Frequency Distribution Table: Living Arrangements

Housing Type

Frequency

Relative Frequency

On Campus

6

0.43

Off Campus

8

0.57

Total

14

1

I believe this table shows the data the best because you are able to see a percentage of the total number of students that are living on vs off of campus. It is an easy break down of the information that gives a clear picture of the results.

I chose a bar chart to represent this data because I believe it gives the best visual representation of the information shown. You can see the difference by just a quick glance to get an overall idea of the situation.

Variable

Ages: 18, 19, 17, 30, 18, 21, 45, 20, 18, 36, 25, 29, 31, 19

Mean: 24.7

Median: 20.5

Mode: 18

I believe that Median is the best measurement for central tendency because it best measures the average age group of college attendants. It gives an idea of the middle man between all data for those attending.

Measure of Dispersion:

Range: 28 years

Standard Deviation: 8.4 years

A narrower deviation would indicate that all of the ages were closer to the median age range of the data. A wider deviation would indicate that the age range extends further out, either younger or older, than the median age range.