College Political Science Quiz: Descriptive Statistics
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Descriptive StatisticsQuestion 1 of 19

An analysis of political participation examined the relationship between age and voting frequency across 500 citizens. The correlation coefficient was r = 0.34. When the sample was split by education level, college graduates (n=220) showed r = 0.28, while non-college graduates (n=280) showed r = 0.41. The overall mean voting frequency was 3.2 elections per decade with a standard deviation of 1.8.

What does the difference in correlation coefficients between education groups suggest about the relationship between age and voting frequency, and how should this inform interpretation of the overall correlation?

Education acts as a suppressor variable that weakens the age-voting relationship among college graduates, suggesting the overall correlation understates the true relationship strength for most citizens.
Education acts as a moderator variable where the age-voting relationship is stronger among non-college graduates, suggesting the overall correlation masks important subgroup differences in relationship strength.
Education acts as a mediating variable that partially explains the age-voting relationship, suggesting the overall correlation overstates the direct effect of age on voting frequency patterns.
Education acts as a confounding variable that artificially inflates the age-voting relationship among college graduates, suggesting the overall correlation represents a spurious association between variables.
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College Political Science Quiz

College Political Science Quiz: Descriptive Statistics

Practice Descriptive Statistics in College Political Science with focused quiz questions that help you check what you know, review explanations, and build confidence with test-style prompts.

What this quiz covers

This quiz focuses on Descriptive Statistics, giving you a quick way to practice the rules, question types, and explanations that matter most for College Political Science.

How to use this quiz

Try each quiz question before looking at the correct answer. Use the explanations to review missed ideas, then come back to similar questions until the pattern feels familiar.

All questions

Question 1

An analysis of political participation examined the relationship between age and voting frequency across 500 citizens. The correlation coefficient was r = 0.34. When the sample was split by education level, college graduates (n=220) showed r = 0.28, while non-college graduates (n=280) showed r = 0.41. The overall mean voting frequency was 3.2 elections per decade with a standard deviation of 1.8.

What does the difference in correlation coefficients between education groups suggest about the relationship between age and voting frequency, and how should this inform interpretation of the overall correlation?

  1. Education acts as a suppressor variable that weakens the age-voting relationship among college graduates, suggesting the overall correlation understates the true relationship strength for most citizens.
  2. Education acts as a moderator variable where the age-voting relationship is stronger among non-college graduates, suggesting the overall correlation masks important subgroup differences in relationship strength. (correct answer)
  3. Education acts as a mediating variable that partially explains the age-voting relationship, suggesting the overall correlation overstates the direct effect of age on voting frequency patterns.
  4. Education acts as a confounding variable that artificially inflates the age-voting relationship among college graduates, suggesting the overall correlation represents a spurious association between variables.
Explanation: The correlation differs substantially between education groups (r = 0.28 for college graduates vs. r = 0.41 for non-college graduates), indicating education moderates the relationship between age and voting. The overall correlation (r = 0.34) falls between these values, masking the fact that age is a stronger predictor of voting frequency among non-college graduates than among college graduates. This suggests different mechanisms may drive political participation across education levels.

Question 2

A study of campaign spending analyzed expenditure data from 180 congressional races. The spending amounts (in thousands) showed the following distribution: minimum = $245K, Q1 = $890K, median = $1,340K, Q3 = $2,180K, maximum = $8,950K, mean = $1,680K. Researchers identified 12 races as statistical outliers using the 1.5×IQR rule.

Given this distribution, what is the most likely composition of the 12 identified outliers, and what does this suggest about the overall shape of the spending distribution?

  1. All 12 outliers are high-spending races above $4,115K, indicating a right-skewed distribution with extreme high-spending campaigns driving up the mean significantly above the median. (correct answer)
  2. Approximately 8 outliers are high-spending races above $4,115K and 4 are low-spending races below $-45K, indicating a roughly symmetric distribution with extreme values on both ends.
  3. All 12 outliers are low-spending races below $-45K, indicating a left-skewed distribution with unusually frugal campaigns driving down the mean below the median substantially.
  4. Approximately 6 outliers are high-spending races above $4,115K and 6 are low-spending races below $-45K, indicating a bimodal distribution with separate clusters of spending patterns.
Explanation: Using the 1.5×IQR rule: IQR = Q3 - Q1 = $2,180K - $890K = $1,290K. Upper fence = Q3 + 1.5×IQR = $2,180K + $1,935K = $4,115K. Lower fence = Q1 - 1.5×IQR = $890K - 1,935K=−1,935K = -1,045K. Since the minimum value is $245K, there can be no low outliers below the lower fence. All outliers must be above 4,115K.Themean(4,115K. The mean (1,680K) being higher than the median ($1,340K) confirms right skew caused by high-spending outliers.

Question 3

A longitudinal study tracked political engagement scores for 300 citizens over 5 years. At baseline, the scores had a mean of 45.2 and standard deviation of 12.8. At year 5, the mean was 52.7 and standard deviation was 16.4. The correlation between baseline and year 5 scores was r = 0.67. Individual change scores (Year 5 - Baseline) had a mean of 7.5 and standard deviation of 11.2.

Using the relationship between the given statistics, what does the pattern of change reveal about the stability and development of political engagement over the 5-year period?

  1. The correlation of 0.67 indicates strong stability in political engagement rankings, while the change score mean of 7.5 represents a practically significant population-level increase in engagement over time.
  2. The change score statistics are inconsistent with the baseline and year 5 statistics, suggesting measurement error or sample attrition that compromises the validity of longitudinal conclusions about engagement stability.
  3. The increased standard deviation from 12.8 to 16.4 indicates growing inequality in political engagement, while the change score variance suggests this divergence was primarily driven by differential growth rates.
  4. The moderate correlation (0.67) combined with increased variance suggests that while relative rankings remained fairly stable, individual trajectories varied considerably, with some citizens showing large increases while others remained static. (correct answer)
Explanation: When analyzing longitudinal data about political behavior, you need to examine both stability (how much individual rankings persist) and change patterns (how the overall distribution shifts). This question tests your ability to interpret multiple statistical indicators together. The correct interpretation emerges from combining all the statistics. The correlation of 0.67 shows moderate stability—people's relative positions are fairly consistent but not locked in place. The increase in standard deviation from 12.8 to 16.4 reveals growing variability in the population. Most tellingly, the change score standard deviation of 11.2 is quite large relative to the mean change of 7.5, indicating substantial individual differences in how much people's engagement changed. This pattern suggests that while rankings stayed somewhat stable, individual trajectories varied considerably—some citizens experienced large increases while others showed little change. Answer A overstates the stability (0.67 is moderate, not strong) and focuses only on average change while ignoring the variability. Answer B incorrectly assumes the statistics are inconsistent—they're actually mathematically coherent and reveal meaningful patterns rather than measurement problems. Answer C correctly identifies growing inequality but wrongly emphasizes "differential growth rates" as the primary driver when the moderate correlation suggests the pattern is more complex. For political science research questions, always examine correlations alongside variance changes and individual difference measures. Don't just look at means—the variability around those means often tells the more interesting story about how political attitudes and behaviors develop over time.

Question 4

A cross-national study examined democratic satisfaction scores (0-10 scale) across 25 countries. The distribution showed: mean = 6.8, median = 7.2, mode = 8.1, variance = 4.41, and range = 8.3. When researchers applied a square root transformation to address distributional issues, the new distribution had: mean = 2.51, median = 2.68, variance = 0.31.

What can be concluded about the effectiveness of the square root transformation in addressing the distributional properties of the original democratic satisfaction data?

  1. The transformation successfully reduced right skew, as evidenced by the new mean being closer to the new median, and substantially reduced variance from 4.41 to 0.31.
  2. The transformation was ineffective at addressing skew, as the new mean is still below the new median, and the variance reduction is simply an artifact of scale compression.
  3. The transformation successfully reduced left skew, as evidenced by the new mean (2.51) being closer to the new median (2.68), and appropriately reduced variance for the new scale. (correct answer)
  4. The transformation overcorrected the original right skew, creating new left skew as shown by the mean-median relationship, while appropriately normalizing the variance structure.
Explanation: When analyzing data transformations in political science research, you need to identify the original distribution's skew and evaluate whether the transformation successfully addressed it. Skew is determined by comparing the mean, median, and mode positions. In the original data, mean (6.8) < median (7.2) < mode (8.1), indicating left skew - the tail extends toward lower values. After the square root transformation, the mean (2.51) moved closer to the median (2.68), showing the transformation reduced the skew while maintaining the same directional relationship. The variance reduction from 4.41 to 0.31 is appropriate for the new scale and indicates improved distributional properties. Option A incorrectly identifies the original distribution as right-skewed when the mean < median < mode pattern clearly shows left skew. Option B misses that the transformation did improve the skew - the mean-median gap narrowed from 0.4 to 0.17 units, and dismisses legitimate variance improvement as mere "scale compression." Option D incorrectly claims overcorrection created new left skew, when the data still shows the same directional pattern as before, just less pronounced. The key insight is that successful transformation doesn't require the mean and median to become identical - it should reduce the magnitude of skew while preserving distributional improvements. The square root transformation appropriately addressed the left skew and normalized the variance. Study tip: Always identify the original skew direction first (mean-median-mode relationship), then check if the transformation moved the statistics closer together while maintaining logical scale adjustments.

Question 5

A comparative study examined voter turnout rates across 50 congressional districts. District A had a turnout rate of 68% with a z-score of +1.25. District B had a turnout rate of 71% with a z-score of +2.10. District C had a turnout rate of 59% with a z-score of -0.85.

If District D has a turnout rate that falls exactly at the 84th percentile of the distribution (assuming normal distribution), what can be determined about District D's turnout rate and z-score?

  1. District D has a turnout rate of approximately 69.2% and a z-score of +1.00, placing it between Districts A and B in relative performance.
  2. District D has a turnout rate of approximately 66.4% and a z-score of +1.00, placing it below District A but above average performance. (correct answer)
  3. District D has a turnout rate of approximately 72.8% and a z-score of +1.00, placing it above District B in absolute but not relative terms.
  4. District D has a turnout rate of approximately 70.5% and a z-score of +1.00, placing it between Districts A and B in both measures.
Explanation: In a normal distribution, the 84th percentile corresponds to a z-score of +1.00. To find the mean and standard deviation: Using District A (68%, z = +1.25): 68 = μ + 1.25σ. Using District C (59%, z = -0.85): 59 = μ - 0.85σ. Solving: 68 - 59 = 1.25σ + 0.85σ, so 9 = 2.10σ, thus σ = 4.29. Then μ = 68 - 1.25(4.29) = 62.64%. For District D: turnout = 62.64 + 1.00(4.29) = 66.93% ≈ 66.4%.

Question 6

A political polling organization collected data on candidate support across 200 precincts. The data showed: 25th percentile = 34%, 50th percentile = 41%, 75th percentile = 48%, mean = 42.8%, standard deviation = 8.6%. A subset analysis of 45 urban precincts revealed: 25th percentile = 38%, 50th percentile = 45%, 75th percentile = 52%, mean = 46.2%, standard deviation = 7.1%.

What does the comparison of the coefficient of variation between the full dataset and urban subset suggest about the relative consistency of candidate support?

  1. Urban precincts show 18.2% relative variability compared to 20.1% for all precincts, indicating more consistent support patterns in urban areas despite higher absolute support levels.
  2. Urban precincts show 18.2% relative variability compared to 15.4% for all precincts, indicating less consistent support patterns in urban areas with disproportionately higher variation.
  3. Urban precincts show 20.1% relative variability compared to 15.4% for all precincts, indicating less consistent support patterns in urban areas despite higher median support levels.
  4. Urban precincts show 15.4% relative variability compared to 20.1% for all precincts, indicating more consistent support patterns in urban areas with proportionally less variation. (correct answer)
Explanation: When analyzing polling data consistency across different geographic areas, the coefficient of variation (CV) is your key tool for comparing relative variability. The CV equals the standard deviation divided by the mean, expressed as a percentage, allowing you to compare consistency even when the groups have different average support levels. Let's calculate both coefficients of variation. For all precincts: CV=8.642.8=0.201=20.1%CV = \frac{8.6}{42.8} = 0.201 = 20.1\%. For urban precincts: CV=7.146.2=0.154=15.4%CV = \frac{7.1}{46.2} = 0.154 = 15.4\%. Since urban precincts have a lower CV (15.4% vs 20.1%), they show more consistent support patterns with proportionally less variation. Answer choice A incorrectly calculates the urban CV as 18.2% and the overall CV as 20.1%. The urban calculation is wrong. Answer choice B uses the same incorrect 18.2% for urban areas but also miscalculates the overall CV as 15.4%, reversing the actual values. Answer choice C compounds errors by claiming urban areas have 20.1% CV (the actual overall figure) and overall areas have 15.4% CV (the actual urban figure), completely swapping the results. Answer choice D correctly identifies urban precincts as having 15.4% relative variability compared to 20.1% for all precincts, properly concluding that urban areas show more consistent support patterns. Remember: coefficient of variation questions test both your calculation skills and interpretation abilities. Always double-check your math and ensure your conclusion matches the direction of the relationship—lower CV means more consistency, regardless of absolute support levels.

Question 7

A political scientist analyzed survey response rates across different demographic groups. Group X (n=150) had a mean response rate of 0.72 with a standard deviation of 0.18. Group Y (n=200) had a mean response rate of 0.68 with a standard deviation of 0.22. When the groups were combined, the overall mean response rate was 0.696.

If a researcher wants to create standardized response rate categories where 'High' represents the top 16% of all individual responses (assuming normal distribution), what standardized score threshold should be used, and how should it be interpreted?

  1. A z-score of +1.00 should be used as the threshold, representing response rates approximately 0.20 standard deviations above the combined mean across both demographic groups.
  2. A z-score of +1.28 should be used as the threshold, representing response rates approximately 1.28 combined standard deviations above the pooled mean of 0.696.
  3. A z-score of +1.00 should be used as the threshold, representing response rates approximately one combined standard deviation above the pooled mean of 0.696. (correct answer)
  4. A z-score of +0.84 should be used as the threshold, representing response rates approximately 0.84 combined standard deviations above the pooled mean of 0.696.
Explanation: When you encounter questions about standardized scores and percentiles in political science research, you're dealing with the normal distribution and z-scores. The key insight is that specific percentiles correspond to specific z-score thresholds regardless of the actual data values. For the top 16% of responses, you need the z-score that leaves 84% below it (since 100% - 16% = 84%). In a standard normal distribution, this corresponds to a z-score of +1.00. This is a fundamental statistical relationship you should memorize: the 84th percentile always equals a z-score of +1.00. Choice C correctly identifies both the z-score (+1.00) and properly interprets it as "approximately one combined standard deviation above the pooled mean of 0.696." Choice A gets the z-score right (+1.00) but incorrectly states it represents "0.20 standard deviations above the mean" when it actually represents exactly 1.00 standard deviation above the mean. Choice B uses z = +1.28, which corresponds to the 90th percentile (top 10%), not the 84th percentile (top 16%). The interpretation is correct for that z-score, but it's the wrong threshold. Choice D uses z = +0.84, which corresponds to roughly the 80th percentile (top 20%), not the 84th percentile we need. Study tip: Memorize key percentile-to-z-score relationships: 84th percentile = z of +1.00, 90th percentile = z of +1.28, and 95th percentile = z of +1.65. These appear frequently in political science research methodology questions.

Question 8

A political scientist conducted a survey of 1,200 registered voters regarding their trust in government institutions. The trust scores (on a scale of 0-100) had a mean of 42.5, a median of 38.0, and a mode of 35.0. The standard deviation was 18.2, and the interquartile range was 24.0. When the researcher excluded responses from voters over age 65, the mean increased to 39.8, the median increased to 36.0, and the standard deviation decreased to 15.4.

Based on the changes in descriptive statistics when older voters are excluded, which conclusion about the original distribution of trust scores is most strongly supported?

  1. Voters over 65 had systematically lower trust scores than younger voters, creating a left-skewed distribution in the original data. (correct answer)
  2. Voters over 65 had systematically higher trust scores with greater variability, creating a right-skewed distribution in the original data.
  3. Voters over 65 had trust scores concentrated around the median, reducing the overall skewness but increasing variability in the original data.
  4. Voters over 65 had bimodal trust score patterns that increased central tendency measures while decreasing dispersion in the original data.
Explanation: When older voters are excluded, both the mean (42.5 → 39.8) and median (38.0 → 36.0) decrease, and the standard deviation decreases (18.2 → 15.4). This indicates that older voters had lower trust scores on average and contributed more variability to the distribution. The original distribution shows mean > median > mode (42.5 > 38.0 > 35.0), indicating right skew. However, when the lower-scoring, more variable older voters are removed, the measures decrease and become less variable, suggesting these voters were pulling the distribution toward lower values with high variability, creating left skew in their segment.

Question 9

A researcher analyzes the number of days a year that a national legislature is in session. For a 50-year period, the statistics are as follows: mean = 160 days, median = 145 days, mode = 140 days.

Based solely on these three measures, what is the most likely shape of the distribution of session days?

  1. A normal, symmetrical distribution.
  2. A negatively skewed (left-skewed) distribution.
  3. A positively skewed (right-skewed) distribution. (correct answer)
  4. A bimodal distribution with two distinct peaks.
Explanation: The relationship between the mean, median, and mode can indicate the skewness of a distribution. When the distribution is positively skewed (has a long tail to the right), the mean is pulled in the direction of the tail, making it larger than the median, which is in turn larger than the mode. The pattern Mean > Median > Mode (160 > 145 > 140) strongly suggests a positive skew, likely caused by some years with exceptionally long legislative sessions.

Question 10

A political scientist studying campaign finance analyzes a dataset of individual donations to a presidential candidate. The vast majority of donations are small, under $100, but there are a few donations in the millions of dollars. The analysis of this distribution of donation amounts yields three measures of central tendency.

Given the described distribution of donations, which of the following relationships between the mean, median, and mode is most likely to be true?

  1. The mean will be approximately equal to the median.
  2. The mean will be greater than the median. (correct answer)
  3. The mean will be less than the median.
  4. The mode will be greater than the mean.
Explanation: This distribution is positively skewed (or skewed to the right) because of the few extremely large donations (outliers). In a positively skewed distribution, the mean is pulled in the direction of the long tail, making it greater than the median. The median is a more robust measure of central tendency in this case. The mode would be the most frequent, small donation amount, making it the smallest of the three measures.

Question 11

A study measures the level of trust in the national legislature on a scale of 0 to 100 for citizens in two countries. In Country X, the mean score is 40 and the standard deviation is 5. In Country Y, the mean score is 50 and the standard deviation is 15.

Based on this information, which of the following is the most accurate conclusion?

  1. The average citizen in Country Y trusts the legislature more than the average citizen in Country X.
  2. A citizen with a trust score of 50 in Country X is more typical than a citizen with a score of 50 in Country Y.
  3. The higher standard deviation in Country Y proves that its political system is less stable than that of Country X.
  4. There is a greater degree of consensus about the legislature among citizens of Country X than Country Y. (correct answer)
Explanation: The standard deviation measures the dispersion or spread of the data around the mean. A smaller standard deviation (5 in Country X) indicates that the data points are clustered more closely around the mean, implying a stronger consensus. A larger standard deviation (15 in Country Y) indicates more variability in opinion. While choice A is true about the means, choice B provides a more nuanced interpretation by incorporating the measure of dispersion. Choice C makes a causal leap that is not supported by the data. Choice D is incorrect; a score of 50 is the mean in Country Y (making it typical), but it is two standard deviations above the mean in Country X (making it atypical).

Question 12

A report on global political freedom ranks countries on a composite score. The report states that a country with a score of 35 is at the 15th percentile.

What is the correct interpretation of the country's ranking?

  1. The country has a political freedom score 15% lower than the global average.
  2. Only 15% of the country's population experiences high levels of political freedom.
  3. 15% of the countries included in the report have a political freedom score of 35 or less. (correct answer)
  4. 85% of the countries included in the report have a political freedom score of 35 or less.
Explanation: A percentile rank indicates the percentage of observations in a dataset that fall at or below a certain value. Being at the 15th percentile means that 15% of the other countries in the dataset have a score equal to or lower than 35. Distractor A confuses percentile with percentage difference from the mean. Distractor B misinterprets the unit of analysis (countries, not people within a country). Distractor D incorrectly calculates the percentage (it describes the 85th percentile).

Question 13

In a comparative study of political engagement, the mean score on a political knowledge quiz was 65 (out of 100) with a standard deviation of 8. A particular respondent, Jordan, scored an 81 on the quiz.

How should Jordan's score be interpreted relative to the sample?

  1. Jordan's score is 16 points above the average, which is not statistically significant.
  2. Jordan's score is in the 81st percentile, meaning 81% of respondents scored lower.
  3. Jordan's score is better than average, but falls within the range of one standard deviation from the mean.
  4. Jordan's score is exceptionally high, falling exactly two standard deviations above the mean. (correct answer)
Explanation: To interpret a single score relative to a distribution, we can calculate a z-score: (individual score - mean) / standard deviation. For Jordan, this is (81 - 65) / 8 = 16 / 8 = 2.0. This means Jordan's score is exactly two standard deviations above the mean, which is considered a relatively high score. Distractor A makes an unsubstantiated claim about significance. Distractor C is incorrect because a score of 81 is outside one standard deviation (65 ± 8, or 57-73). Distractor D incorrectly equates the raw score with a percentile rank.

Question 14

A political scientist is using a 10-point scale to measure ideological self-placement, where 1 is 'Strongly Liberal' and 10 is 'Strongly Conservative'. To simplify analysis, the researcher decides to transform the scale by adding 5 to every respondent's score. The standard deviation of the original scores was 2.5.

After the transformation, what will be the standard deviation of the new ideological scores?

  1. 2.5 (correct answer)
  2. 7.5
  3. 5.0
  4. 12.5
Explanation: Standard deviation is a measure of dispersion, or how spread out the data points are from the mean. Adding a constant to every value in a dataset shifts the entire distribution up or down the number line, changing the mean, but it does not change the distances between the data points or their distance from the new mean. Therefore, the spread of the data remains the same, and the standard deviation is unchanged. The new standard deviation will still be 2.5.

Question 15

A researcher is analyzing public opinion on a highly divisive social issue using a survey where respondents place themselves on a scale from 1 (strongly oppose) to 10 (strongly support). The analysis reveals a bimodal distribution with significant clusters of respondents at scores of 2 and 9. The calculated mean score for the entire sample is 5.5.

What is the most methodologically sound interpretation of these descriptive statistics?

  1. The mean score of 5.5 indicates that the average citizen is moderate or undecided on this issue.
  2. The population is polarized into two distinct groups, making the mean a potentially misleading measure of central tendency. (correct answer)
  3. The distribution is negatively skewed because of the large number of respondents at the lower end of the scale.
  4. The large range between the two peaks suggests a high standard deviation, which confirms a lack of public consensus.
Explanation: A bimodal distribution indicates two distinct peaks, or modes, suggesting that the population is polarized into two different groups. In such cases, the mean, which falls between the peaks, does not accurately represent a 'typical' individual's opinion. Choice A is a common misinterpretation of the mean. Choice C is incorrect because bimodality is distinct from skewness. Choice D is plausible but B offers a more complete interpretation of the situation described.

Question 16

A political scientist is studying judicial confirmations and finds that the time from nomination to confirmation for federal judges is highly right-skewed due to a few exceptionally long and contentious confirmation processes. The researcher wants to provide a summary of the typical confirmation time and its variability that is not unduly influenced by these extreme outliers.

Which pair of descriptive statistics would be most appropriate for the researcher to use?

  1. Mean and standard deviation
  2. Median and interquartile range (correct answer)
  3. Mode and range
  4. Mean and range
Explanation: In a skewed distribution with significant outliers, the mean and standard deviation (and range) are heavily influenced by the extreme values. The median (the 50th percentile) and the interquartile range (the distance between the 25th and 75th percentiles) are 'robust' or 'resistant' measures, meaning they are not significantly affected by outliers. Therefore, they provide a more accurate summary of the central tendency and spread for this type of data.

Question 17

A researcher compiles a dataset of the ages of 101 members of a country's national assembly. The mean age is calculated to be 60. Later, a data entry error is found: one member listed as 9 years old should have been 90 years old.

How will the correction of this single data point affect the dataset's mean and median?

  1. The mean will increase significantly, while the median will likely remain the same or change by one position. (correct answer)
  2. Both the mean and the median will increase by a substantial and roughly equal amount.
  3. The median will increase significantly, while the mean will remain relatively stable.
  4. The mean will decrease, and the median will increase.
Explanation: The mean is sensitive to the actual value of all data points, including outliers. Changing a value from 9 to 90 is a large increase (81), which will be averaged across all 101 members, causing a significant increase in the mean. The median, however, is the value of the middle observation when the data are ordered. Correcting this one value from a low outlier to a high outlier is unlikely to change which observation is in the middle position, or at most shift it to the next value in the sorted list. Therefore, the median is robust to this type of error.

Question 18

A political scientist analyzes 10,000 individual campaign contributions to a mayoral candidate. The analysis yields the following descriptive statistics: Mean = $550, Median = $50, Mode = $25, and Standard Deviation = $2,500. Given this information, which of the following is the most reasonable inference about the distribution of donations?

  1. The distribution is positively skewed, with a small number of very large donations increasing the mean. (correct answer)
  2. The distribution is negatively skewed, as the median value is significantly lower than the mean.
  3. Most individual contributions were close to $550, but the large standard deviation indicates high variability.
  4. The mode of $25 suggests that the data are unreliable, as the most frequent value is far from the average.
Explanation: The correct answer is A. In a distribution of data, the mean is sensitive to outliers, while the median is resistant. When the mean is substantially larger than the median (here, $550 >> 50),itindicatesthattherearehigh−valueoutlierspullingtheaverageup.Thispatternischaracteristicofapositive(orright)skew.Inthecontextofcampaignfinance,thissuggestsalargenumberofsmalldonationsandasmallnumberofverylargedonationsthatinflatethemean.Bisincorrectbecauseameangreaterthanthemedianindicatesapositive,notnegative,skew.Cisincorrectbecauseinahighlyskeweddistribution,themeanisnotagoodmeasureofcentraltendency;themedian(50), it indicates that there are high-value outliers pulling the average up. This pattern is characteristic of a positive (or right) skew. In the context of campaign finance, this suggests a large number of small donations and a small number of very large donations that inflate the mean. B is incorrect because a mean greater than the median indicates a positive, not negative, skew. C is incorrect because in a highly skewed distribution, the mean is not a good measure of central tendency; the median (50) gives a much better sense of the 'typical' donation. D is incorrect because the mode simply represents the most frequent value and its distance from the mean is a feature of the skewed distribution, not an indicator of data unreliability.

Question 19

A survey on public trust in the national legislature was conducted in Country A and Country B, measured on a scale of 0 to 100. The results were as follows: Country A had a mean trust score of 60 with a standard deviation of 5. Country B had a mean trust score of 50 with a standard deviation of 10. A respondent from Country A reported a trust score of 70, while a respondent from Country B reported a score of 65. Which of the following statements correctly compares their relative levels of trust?

  1. The respondent from Country B expressed higher trust relative to their national context because their score was 15 points above their country's mean.
  2. The respondent from Country A expressed higher trust relative to their national context, as their score was two standard deviations above their country's mean. (correct answer)
  3. Both respondents expressed an equally high level of relative trust because their scores are in the top quintile of their respective countries.
  4. A meaningful comparison is not possible because the different standard deviations indicate that the scales are not directly comparable.
Explanation: The correct answer is B. To compare values from different distributions, we must standardize them by calculating their z-scores (z = (score - mean) / standard deviation). For the respondent from Country A: z = (70 - 60) / 5 = 10 / 5 = 2.0. This means their score is 2.0 standard deviations above the mean for Country A. For the respondent from Country B: z = (65 - 50) / 10 = 15 / 10 = 1.5. This means their score is 1.5 standard deviations above the mean for Country B. Since 2.0 > 1.5, the respondent from Country A expressed a higher level of trust relative to their national average. A is incorrect because it compares the raw deviation from the mean (10 points vs. 15 points) without accounting for the different levels of dispersion (standard deviation) in each country. C is incorrect as we do not have enough information to determine quintiles and relative trust is best measured by standard deviations. D is incorrect because standardization using z-scores is the correct statistical procedure for making exactly this type of comparison across distributions with different parameters.