ALC 9/9

Reporting the Mean, Median, and Mode

The descriptive statistics for the variable Age of Respondent (N = 600, Missing = 1) are as follows:

Mean: 47.10

Median: 45.00

Mode: 30

These measures of central tendency offer distinct insights into age distribution within the sample. Frankfort-Nachmias, Leon-Guerrero, and Davis (2020) explain that the mean reflects the arithmetic average, the median identifies the midpoint, and the mode indicates the most frequently occurring value (p. 78).

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                                                                         The Better Measure for Central Tendency and Why?

Given the slightly right-skewed distribution observed in the histogram, the median emerges as the most appropriate measure of central tendency. A small number of older respondents elevates the mean, while the mode (30) is notably lower than both the mean and median, suggesting it does not represent the central mass of the data. Frankfort-Nachmias et al. (2020) emphasize that the median is more robust in skewed distributions because it is unaffected by extreme values (p. 90). Therefore, the median offers a more accurate reflection of the “typical” respondent in this dataset.

                                                                                      Report the Standard Deviation

The standard deviation for Age is 16.89, which quantifies the average deviation of individual ages from the mean. This measure provides insight into the degree of dispersion within the dataset (Frankfort-Nachmias et al., 2020, p. 115).

The standard deviation of 16.89 indicates a moderate to high variability in the age distribution. This suggests that respondents’ ages are widely dispersed around the mean, reflecting a heterogeneous sample. According to Frankfort-Nachmias et al. (2020), variability is essential for understanding the spread and reliability of data, and a higher standard deviation implies greater diversity within the population (pp. 113–114). Wagner (2020) also notes that variability should be clearly presented to support transparent and meaningful interpretation of statistical output (p. 137).

                                                                                     How Would You Describe This Data

The age data is moderately skewed, with a central tendency toward middle adulthood. The distribution is not symmetrical, as evidenced by the mean being higher than the median and mode. The histogram confirms this visual asymmetry. Most respondents fall between 20 and 60 years old, indicating a broad age range and a diverse sample. Wagner (2020) underscores the importance of presenting such data clearly, especially when preparing it for scholarly communication or policy-relevant analysis (p. 142).

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                                                                                      Categorical Variable Analysis

The variable Political Party Affiliation yielded 596 valid responses and five missing cases. The distribution spans eight distinct categories, with the largest group identifying as Independent (n = 139, 23.3%), followed by Not Strong Democrat (n = 95, 15.9%) and Strong Democrat (n = 90, 15.1%). Smaller segments include Not Strong Republican (12.2%), Strong Republican (9.6%), Independent, Near Democrat (13.4%), Independent, Near Republican (8.2%), and Other Party (2.2%). This distribution reflects a politically diverse sample, with no single category dominating the landscape. As Frankfort-Nachmias, Leon-Guerrero, and Davis (2020) note, frequency distributions are essential for summarizing categorical data and identifying patterns in group identity (p. 78).

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                                                                                  Appropriate Action of Variation

For nominal-level data, the variation ratio is the most appropriate measure of dispersion. This result indicates that approximately 77% of respondents selected a category other than the modal response (Independent), suggesting a high degree of political diversity. According to Frankfort-Nachmias et al. (2020), a higher variation ratio reflects greater heterogeneity in categorical data, which is critical for understanding the complexity of social identity and ideological alignment (p. 125). The variation ratio of 0.77 confirms that the data are highly variable, with respondents distributed across a broad spectrum of political affiliations. This level of dispersion enhances the analytical richness of the dataset and supports nuanced interpretations of political behavior.  

                                       Was the presentation of results clear? If so, provide some specific comments on why. If not, provide constructive suggestions.

Are you able to understand how the results might relate back to positive social change? Do you think there are other aspects of positive social change related to the results?