Question

The college administration is considering a total ban on student automobiles. You have conducted a poll on this issue of 20 fellow students and 20 of the neighbors who live around the campus and have calculated scores for your respondents. On the scale you used, a high score indicates strong opposition to the proposed ban. The scores are presented here for both groups. Calculate an appropriate measure of central tendency and compare the two groups in a sentence or two. \(\begin{array}{rrrr} \hline {\text { Students }} & & {\text { Neighbors }} \\ \hline 10 & 11 & 0 & 7 \\ 10 & 9 & 1 & 6 \\ 10 & 8 & 0 & 0 \\ 10 & 11 & 1 & 3 \\ 9 & 8 & 7 & 4 \\ 10 & 11 & 11 & 0 \\ 9 & 7 & 0 & 0 \\ 5 & 1 & 1 & 10 \\ 5 & 2 & 10 & 9 \\ 0 & 10 & 10 & 0 \\ \hline \end{array}\)

Short answer

Both students and neighbors have an average score of 7.8, indicating similar opposition levels to the proposed ban.

Step-by-step solution

- Organize the Data

Firstly, let's list down the scores of the students and the neighbors separately to have a clear view of the data. Students: 10, 10, 10, 10, 9, 10, 9, 5, 5, 0 Neighbors: 11, 9, 8, 11, 8, 11, 7, 1, 2, 10

- Calculate the Mean for Students

To find the mean score for students, sum all the scores and divide by the number of students. The total sum of students' scores is 10 + 10 + 10 + 10 + 9 + 10 + 9 + 5 + 5 + 0 = 78. There are 10 students, so the mean is \( \frac{78}{10} = 7.8 \)

- Calculate the Mean for Neighbors

To find the mean score for neighbors, sum all the scores and divide by the number of neighbors. The total sum of neighbors' scores is 11 + 9 + 8 + 11 + 8 + 11 + 7 + 1 + 2 + 10 = 78. There are 10 neighbors, so the mean is \( \frac{78}{10} = 7.8 \)

- Compare the Two Groups

Both the students and the neighbors have the same mean score of 7.8. This indicates that, on average, both groups have a similar level of opposition to the proposed ban on student automobiles.

Key concepts

Mean Calculation

The mean, often referred to as the average, is a key measure of central tendency. To calculate the mean, you first sum all the values in your data set. Then you divide this total by the number of values.
In the student poll example, we calculated the mean for both the student scores and the neighbor scores. Here, the sums of both groups' scores were the same: 78. By dividing this total by the number of participants (10 in each group), we determined that both students and neighbors had a mean score of 7.8. This indicates a similar average sentiment in both groups regarding the proposed ban.

Data Organization

Organizing data effectively is the foundation for any analysis. In our exercise, we listed the scores of students and neighbors separately to have a clear, structured view.
To do this, you simply list the scores in a sequential manner or in a table. Clear data organization makes it easier to perform calculations and analyze trends. For this exercise, listing the data for both groups allowed us to quickly calculate the mean and see both individual and combined tendencies.
Organizing data can also help in spotting any outliers or unique patterns that may need further investigation or understanding.

Central Tendency Comparison

Central Tendency measures like the mean, median, and mode help summarize a set of data points with a single value that represents the center point or typical value.
In this case, we used the mean to compare the central tendency of students' and neighbors' attitudes towards the proposed ban. Despite individual score variations, the mean provided a clear, concise way to grasp the overall sentiment of each group.
When comparing the central tendencies, similar means (like the 7.8 found for both groups here) indicate comparable general attitudes. However, it’s essential to note that using other measures like median and mode can sometimes provide additional insights, especially if the data set includes outliers.

Student Poll Analysis

Analyzing student poll results involves multiple steps including gathering, organizing, and calculating central tendency measures.
In our example, we first collected the scores indicating opposition to a ban on student automobiles. After organizing these scores, we calculated the mean.
The student poll results, with a mean score of 7.8, suggest a moderate to strong opposition to the automobile ban. This numerical value encapsulates the overall sentiment of the polled students.
Poll analysis helps in understanding and summarizing the general preferences or opinions on a given topic in an easily digestible numerical form.

Neighbor Poll Analysis

Similarly, analyzing neighbor poll results also requires organizing the data and calculating measures like the mean.
In this exercise, we gathered scores indicating the neighbors' opposition to the student automobile ban. We then calculated a mean score, which also turned out to be 7.8.
This outcome suggests that, similar to students, the neighbors also have a moderate to strong opposition to the proposed ban. By calculating and comparing these scores, we can infer that both students and neighbors share similar views on the issue.
Such analysis is crucial for understanding community sentiment and can help in making informed decisions or policy recommendations.