Math 1 Quiz: Outlier Effects On Center
20 questions · exam conditions
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Outlier Effects On CenterQuestion 1 of 20

A company's salary data shows that when the CEO's salary is included, the mean salary is $95,000 and the median is $52,000. When the CEO's salary is excluded, the mean becomes $48,000 and the median becomes $51,000. What does this reveal about using these measures to represent typical employee compensation?

The mean with CEO included better represents overall company compensation since it accounts for all employees and shows the total resources
The median with CEO excluded provides the most accurate picture since it eliminates bias and represents the true center of employee salaries
The median with CEO included better represents typical employee salary since it's resistant to the extreme high salary of the CEO
The mean with CEO excluded better represents typical compensation since it eliminates the outlier effect while maintaining mathematical precision
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Math 1 Quiz

Math 1 Quiz: Outlier Effects On Center

Practice Outlier Effects On Center in Math 1 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 Outlier Effects On Center, giving you a quick way to practice the rules, question types, and explanations that matter most for Math 1.

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.

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Question 1

A company's salary data shows that when the CEO's salary is included, the mean salary is $95,000 and the median is $52,000. When the CEO's salary is excluded, the mean becomes $48,000 and the median becomes $51,000. What does this reveal about using these measures to represent typical employee compensation?

  1. The mean with CEO included better represents overall company compensation since it accounts for all employees and shows the total resources
  2. The median with CEO excluded provides the most accurate picture since it eliminates bias and represents the true center of employee salaries
  3. The median with CEO included better represents typical employee salary since it's resistant to the extreme high salary of the CEO (correct answer)
  4. The mean with CEO excluded better represents typical compensation since it eliminates the outlier effect while maintaining mathematical precision
Explanation: The median is resistant to outliers, so even with the CEO's extremely high salary included, it only changed from $51,000 to $52,000, still representing where a typical employee falls. The mean jumped dramatically from $48,000 to $95,000 with the CEO included, making it misleading for representing typical employee compensation. Choice A confuses total resources with typical values. Choice B unnecessarily excludes the CEO when the median can handle the outlier. Choice D incorrectly suggests the mean is more precise when it's actually more distorted by the outlier.

Question 2

A dataset has 15 values with a mean of 24 and a median of 26. If the three largest values are increased by 10 each, what will happen to the mean and median, and what does this suggest about their resistance to changes in extreme values?

  1. The mean will increase by 2 and the median will stay the same, showing that median is more resistant to extreme value changes (correct answer)
  2. The mean will increase by 10 and the median will increase by 10, showing both measures are equally affected by extreme value changes
  3. The mean will increase by 2 and the median will increase by 5, showing that mean is more resistant to extreme value changes
  4. The mean will stay the same and the median will increase by 2, showing that mean is more resistant to extreme value changes
Explanation: When the three largest values increase by 10 each, the total increases by 30, so the mean increases by 30/15 = 2. The median is the 8th value (middle of 15), and since only the three largest values changed, the 8th value remains unchanged, so the median stays at 26. This demonstrates that the median is resistant to changes in extreme values while the mean is affected by all changes. Choice B incorrectly suggests both measures change equally. Choices C and D incorrectly describe which measure is more resistant and the actual changes that occur.

Question 3

Two datasets have identical medians of 50. Dataset A has a mean of 48, while Dataset B has a mean of 52. If one extreme outlier is removed from each dataset, which statement best describes the expected changes?

  1. Dataset A likely had a high outlier removed, so its mean will increase toward the median while the median stays relatively stable
  2. Dataset A likely had a low outlier removed, so its mean will increase toward the median while the median stays relatively stable (correct answer)
  3. Dataset B likely had a low outlier removed, so its mean will decrease toward the median while the median stays relatively stable
  4. Both datasets will show equal changes in mean and median since they started with the same median value initially
Explanation: Since Dataset A has a mean (48) below its median (50), it likely contains low outliers pulling the mean down. Removing a low outlier would increase the mean toward the median. Dataset B has a mean (52) above its median (50), suggesting high outliers pulling the mean up. The median is resistant to outliers and would remain relatively stable in both cases. Choice A incorrectly identifies the type of outlier in Dataset A, Choice C incorrectly identifies the outlier type in Dataset B, and Choice D ignores the different relationships between mean and median.

Question 4

A quality control manager notices that when she removes the 5% most extreme measurements from her dataset, the mean changes from 15.2 to 14.8, but the median changes from 14.5 to 14.6. What strategy should she use for reporting typical product quality?

  1. Report the original mean (15.2) because it includes all data points and provides the most complete statistical representation of quality
  2. Report the adjusted mean (14.8) because removing extreme outliers provides a more accurate measure of typical manufacturing performance
  3. Report the original median (14.5) because it naturally resists outlier effects and represents typical quality without data manipulation (correct answer)
  4. Report the adjusted median (14.6) because it combines outlier resistance with the precision of removing confirmed extreme measurements
Explanation: The median's minimal change (14.5 to 14.6) when removing extreme values shows it's already resistant to outliers, while the mean's larger change (15.2 to 14.8) shows it was being influenced by those extreme values. Using the original median avoids the need to subjectively decide which data points to exclude while still providing a measure resistant to outliers. Choice A ignores the outlier problem. Choice B requires arbitrary decisions about what to exclude. Choice D unnecessarily combines two approaches when the original median already handles outliers well.

Question 5

A dataset contains 20 values. When arranged in order, the 10th value is 85 and the 11th value is 87, giving a median of 86. If the five smallest values are each decreased by 15, which statement correctly describes the effect on the measures of center?

  1. The median will remain 86 and the mean will decrease, demonstrating that median is more stable for representing central tendency
  2. The median will decrease to 83 and the mean will decrease by 15, showing both measures are equally sensitive to extreme changes
  3. The median will increase to 89 and the mean will stay the same, demonstrating that changes in extreme values are self-correcting
  4. The median will remain 86 and the mean will decrease by 3.75, showing that extreme values affect mean more than median (correct answer)
Explanation: When you encounter questions about how data changes affect measures of center, focus on understanding that the median depends only on middle values while the mean uses every data point. With 20 values, the median is the average of the 10th and 11th values: 85+872=86\frac{85 + 87}{2} = 86. When you decrease the five smallest values by 15, these values remain the smallest (they just become more negative), so the 10th and 11th positions don't change. The median stays 86. For the mean, decreasing five values by 15 reduces the total sum by 5×15=755 \times 15 = 75. Since this decrease is spread across 20 values, the mean drops by 7520=3.75\frac{75}{20} = 3.75. This demonstrates that extreme values significantly impact the mean while leaving the median unaffected. Choice A incorrectly suggests the mean will decrease without specifying by how much, missing the precise calculation needed. Choice B makes two errors: it claims the median changes (it doesn't, since we're not altering the middle values) and that the mean decreases by the full 15 (it only decreases by 3.75 since the change affects just 5 of 20 values). Choice C is completely backwards, suggesting the median increases and mean stays constant, which contradicts how these measures actually behave. Remember this key distinction: the median only cares about position and is resistant to extreme value changes, while the mean incorporates every data point and shifts proportionally when any values change.

Question 6

A pharmaceutical company tests reaction times for a new medication. The original dataset has mean = 2.4 seconds, median = 2.2 seconds. After discovering and correcting three data entry errors where values were recorded as 0.8, 0.9, and 1.1 seconds instead of 8.0, 9.0, and 11.0 seconds, which changes would you expect?

  1. Mean will increase significantly, median will increase slightly, confirming that mean is more sensitive to extreme values than median (correct answer)
  2. Mean will decrease significantly, median will decrease slightly, showing that both measures are affected similarly by data corrections
  3. Both mean and median will increase by the same amount since the errors affected the same number of data points
  4. Mean will increase slightly, median will increase significantly, demonstrating that median is more sensitive to changes in data values
Explanation: The corrections change low values (0.8, 0.9, 1.1) to high values (8.0, 9.0, 11.0), adding 21.6 seconds total to the dataset. This will increase the mean significantly. Since these were originally among the smallest values and become among the largest, the median (middle value) will increase only slightly as the middle position shifts but not dramatically. This demonstrates the mean's greater sensitivity to extreme values. Choice B has the wrong direction. Choice C incorrectly assumes equal effects. Choice D reverses which measure is more sensitive.

Question 7

A researcher has two datasets with identical ranges and standard deviations. Dataset P has mean = 100, median = 95. Dataset Q has mean = 100, median = 105. If both datasets have one outlier removed, which prediction is most accurate?

  1. Dataset P will show a larger mean change than Dataset Q due to greater outlier influence
  2. Dataset P likely has a high outlier; removing it will decrease the mean and increase the median (correct answer)
  3. Dataset Q likely has a low outlier; removing it will increase the mean and decrease the median
  4. Both datasets will show identical changes since they have matching summary statistics initially
Explanation: Dataset P has mean > median (100 > 95), indicating high outliers pulling the mean up. Removing a high outlier would decrease the mean toward the median. The median might increase slightly as the middle position could shift to a higher value. Dataset Q has mean < median (100 < 105), indicating low outliers. Choice A doesn't specify the direction of change. Choice C correctly identifies Q's outlier type but the question asks about both datasets. Choice D ignores the different mean-median relationships despite identical summary statistics.

Question 8

A researcher studies home prices in two neighborhoods. In Neighborhood X, the mean price is $450,000 and the median is $420,000. In Neighborhood Y, the mean price is $380,000 and the median is $390,000. Based on these measures, which neighborhood likely has more extreme outliers, and which measure should be used to represent typical home prices?

  1. Neighborhood X has more extreme outliers, and the median should be used because it better represents typical prices in both neighborhoods (correct answer)
  2. Neighborhood Y has more extreme outliers, and the mean should be used because it accounts for all price variations in the market
  3. Neighborhood X has more extreme outliers, and the mean should be used because it shows the true average investment value
  4. Both neighborhoods have similar outlier effects, so either measure would be equally appropriate for representing typical home values
Explanation: Neighborhood X shows mean > median ($450K > 420K),indicatinghighoutlierspullingthemeanup.NeighborhoodYshowsmean<median(420K), indicating high outliers pulling the mean up. Neighborhood Y shows mean < median (380K < 390K),indicatinglowoutliers,butthedifferenceissmaller(390K), indicating low outliers, but the difference is smaller (10K vs $30K), suggesting less extreme outlier effects in Y than X. The median is preferred because it's resistant to these outliers and better represents typical prices. Choice B incorrectly identifies which neighborhood has more extreme outliers. Choice C wrongly recommends the mean despite outlier effects. Choice D ignores the clear differences in mean-median relationships.

Question 9

A social media analyst finds that post engagement data has a mean of 1,250 likes and a median of 890 likes. After removing posts with over 10,000 likes (3% of all posts), the mean becomes 920 likes and the median becomes 885 likes. What conclusion about measure selection is most justified?

  1. The original median (890) best represents typical engagement because it was minimally affected by the viral posts that skewed the mean (correct answer)
  2. The adjusted mean (920) best represents typical engagement because it eliminates outlier bias while maintaining computational accuracy
  3. The original mean (1,250) best represents engagement because it includes the viral potential that's important for social media analysis
  4. The adjusted median (885) best represents typical engagement because it combines outlier resistance with the precision of outlier removal
Explanation: The original median of 890 likes was barely affected by removing the viral posts (dropped only 5 likes to 885), while the mean dropped dramatically from 1,250 to 920 (a decrease of 330 likes). This demonstrates the median's resistance to outliers - it already represented typical engagement without needing to exclude data. The small change in median confirms that 890 was already a good measure of typical engagement. Choice B unnecessarily excludes data when the median already handles outliers. Choice C includes misleading outlier effects. Choice D unnecessarily combines approaches.

Question 10

A small startup company has 8 employees. Their annual salaries are: $45,000, $48,000, $52,000, $55,000, $58,000, $62,000, $65,000, and $180,000.

The company is preparing a report for potential investors about employee compensation. If they want to present the most representative picture of what a typical employee earns, which measure should they use and why?

  1. Use the mean ($70,625) because investors need to see the true average cost of human resources for accurate financial planning
  2. Use the median ($56,500) because it represents what a typical employee actually earns, unaffected by the one extremely high salary (correct answer)
  3. Use both measures together because the mean shows total compensation costs while the median shows typical individual earnings
  4. Use the mean ($70,625) because it's mathematically more precise and provides a complete picture of compensation distribution patterns
Explanation: The median ($56,500, average of 4th and 5th values: $55,000 and $58,000) better represents typical employee earnings because 7 of 8 employees earn between $45,000-$65,000. The mean of $70,625 is heavily skewed by the $180,000 outlier salary. For representing 'typical' earnings, the median is superior because it's resistant to this extreme value. Choice A focuses on total costs rather than typical earnings. Choice C is partially correct but doesn't directly answer which single measure is most representative. Choice D incorrectly claims mathematical precision makes the mean better when it's actually distorted.

Question 11

An economist studying income inequality finds that in City A, the mean household income is $75,000 and median is $52,000. In City B, the mean is $68,000 and median is $66,000. Which city likely has greater income inequality, and which measure better represents typical household income in each city?

  1. City A has greater inequality; use median for City A (52,000)andmeanforCityB(52,000) and mean for City B (68,000) to represent typical incomes
  2. City B has greater inequality; use mean for both cities since it accounts for the full income distribution in economic analysis
  3. Both cities have similar inequality; the choice between mean and median depends on whether you want to include high earners or not
  4. City A has greater inequality; use median for both cities since it better represents typical household income regardless of outliers (correct answer)
Explanation: When you encounter questions about income distribution, focus on the relationship between mean and median to assess inequality and determine which measure best represents "typical" income. To identify inequality, compare the mean and median. In City A, the mean (75,000)issignificantlyhigherthanthemedian(75,000) is significantly higher than the median (52,000) - a 23,000gap.InCityB,themean(23,000 gap. In City B, the mean (68,000) and median ($66,000) are very close - only a $2,000 difference. When the mean exceeds the median by a large amount, it indicates positive skew caused by high-income outliers pulling the average upward. City A clearly has greater income inequality. For representing typical income, the median is generally more reliable because it's the middle value - half of households earn more, half earn less. The mean gets distorted by extreme values, especially in skewed distributions like income data. Answer A is wrong because it suggests using different measures for different cities and incorrectly recommends the mean for City B. Answer B incorrectly identifies City B as having greater inequality and assumes the mean is always better for economic analysis. Answer C is wrong because the cities don't have similar inequality - City A's large mean-median gap clearly indicates much greater inequality than City B's small gap. Answer D correctly identifies that City A has greater inequality and recommends using the median for both cities to represent typical household income, since medians aren't affected by high-earning outliers. Remember: When mean > median significantly, expect high inequality and use median for "typical" values.

Question 12

A teacher calculates that removing the lowest test score from her class data changes the mean from 78 to 82 but changes the median from 80 to 81. She concludes that the median is a better measure of center for this dataset. Which reasoning best supports her conclusion?

  1. The median showed less change, indicating it provides a more stable and representative measure of student performance than the mean
  2. The median increased less than the mean, proving it's mathematically more accurate for educational assessment purposes in all cases
  3. The median's smaller change shows that most students scored near 80, while the mean was heavily influenced by the extremely low score (correct answer)
  4. The median became closer to the original mean after removing the outlier, demonstrating better consistency in measurement techniques
Explanation: The large change in mean (4 points) compared to the small change in median (1 point) when removing one low score indicates that the mean was heavily influenced by that extreme value. This suggests the median better represents where most students actually performed. Choice A is partially correct but doesn't explain why the stability matters. Choice B overgeneralizes to 'all cases' and incorrectly uses 'mathematically more accurate.' Choice D focuses on convergence rather than the resistance to outliers that makes median preferable here.

Question 13

A pharmaceutical company testing a new drug finds that most patients show improvement within 5-8 days, but three patients required 45, 52, and 61 days respectively. When reporting efficacy to doctors, the company debates between reporting mean time to improvement (18.3 days) versus median time (6.5 days). Which approach better serves medical decision-making?

  1. The mean of 18.3 days because it provides a comprehensive view that includes patients who may experience delayed response to treatment
  2. The mean of 18.3 days because it provides a more conservative timeline that prevents doctors from setting unrealistic patient expectations
  3. Both measures should be reported as equally valid since they each capture different mathematical properties of the same dataset
  4. The median of 6.5 days because it accurately represents the timeline most patients can expect, while noting outliers separately for complete information (correct answer)
Explanation: When analyzing medical data, you need to consider which statistical measure best represents what typical patients will experience, especially when outliers are present. The correct answer is D because the median of 6.5 days accurately reflects what most patients can expect. Since the majority of patients improved within 5-8 days, the median captures this typical experience without being skewed by the three patients who took much longer (45, 52, and 61 days). For medical decision-making, doctors need realistic expectations for patient counseling, and 6.5 days represents the actual timeline most patients will experience. Mentioning the outliers separately ensures complete transparency without distorting the central tendency. Answer A is wrong because while the mean does include all patients, the 18.3-day average creates a misleading picture—it suggests most patients take nearly three weeks to improve when actually most improve in about a week. Answer B incorrectly calls 18.3 days "conservative"—it's actually inflated by outliers and would lead to overly pessimistic patient expectations. Answer C is wrong because while both measures are mathematically valid, they're not equally useful for medical decisions. The context matters: doctors need to know what's typical, not just mathematical completeness. Remember that when extreme outliers are present in medical or real-world data, the median often provides a more meaningful picture of typical outcomes than the mean. Always consider what information will be most useful for the intended audience's decision-making needs.

Question 14

A social media analytics team finds that most posts receive 10-50 likes, but a few viral posts received over 10,000 likes each. When presenting engagement metrics to stakeholders, they must choose between mean engagement (420 likes) and median engagement (28 likes). Based on the outlier effect, which presentation strategy is most appropriate?

  1. Present the mean of 420 likes to demonstrate the platform's potential for viral content and attract content creators seeking high engagement
  2. Present both measures with equal emphasis since they represent different but equally valid perspectives on platform engagement patterns
  3. Present the median of 28 likes to give content creators realistic expectations about typical post performance, while separately highlighting viral success stories (correct answer)
  4. Present the mean of 420 likes because it accounts for all user activity and provides a more complete picture of total platform engagement
Explanation: When you encounter a dataset with extreme outliers, understanding how they affect the mean versus median is crucial for making ethical data presentation decisions. In this scenario, the few viral posts with 10,000+ likes create severe positive skew. The mean (420 likes) is pulled dramatically upward by these outliers, while the median (28 likes) remains anchored to the typical user experience since most posts receive 10-50 likes. The median better represents what content creators can realistically expect. Answer C is correct because it prioritizes giving content creators accurate expectations about typical performance (median of 28 likes) while acknowledging viral successes separately. This approach is both honest and practical—creators can plan realistic content strategies while understanding that viral hits, though rare, do happen. Answer A is problematic because presenting only the mean of 420 likes would mislead creators about typical performance, potentially causing unrealistic expectations and poor strategic decisions. Answer B treats both measures as equally valid, but in heavily skewed distributions, the mean can be deeply misleading when used alone. Context matters—stakeholders need realistic expectations, not statistical ambiguity. Answer D incorrectly suggests the mean provides a "more complete picture." While the mean does account for all activity mathematically, it obscures the typical user experience when extreme outliers dominate the calculation. Study tip: When you see questions about skewed data with outliers, remember that the median protects against misleading conclusions, while the mean gets "hijacked" by extreme values. Always consider your audience's need for realistic versus comprehensive information.

Question 15

A data analyst notices that adding a single extreme value to a dataset changes the mean by 15 units but changes the median by only 2 units. If the original dataset had 20 values, which statement best explains this phenomenon and its implications for data interpretation?

  1. The extreme value was close to the original median, so the mean is more reliable for this dataset because it incorporates all values equally
  2. The extreme value was far from the center of the data, demonstrating that the median is more robust to outliers and better represents the typical value (correct answer)
  3. The median changed less because it only considers the middle values, making the mean more accurate since it reflects the true center after including all data points
  4. Both measures are equally affected by outliers, so the difference indicates a calculation error rather than a meaningful distinction between the measures
Explanation: The large change in mean (15 units) versus small change in median (2 units) demonstrates that the extreme value was an outlier far from the center. The median is resistant to outliers because it only depends on the middle value(s), while the mean is pulled toward extreme values. This makes the median more robust and better at representing the typical value when outliers are present. Choice A incorrectly suggests the mean is more reliable. Choice C misunderstands that the mean being affected more doesn't make it more accurate. Choice D incorrectly states both measures are equally affected.

Question 16

A researcher studying income data for a small town finds that removing the three highest earners changes the mean income from $68,000\$68{,}000 to $52,000\$52{,}000 but changes the median from $48,000\$48{,}000 to $47,000\$47{,}000. Based on this information, which conclusion about the income distribution is most justified?

  1. The income distribution is approximately symmetric since both the mean and median decreased when outliers were removed
  2. The three highest earners are outliers that significantly skew the distribution, and the median better represents typical income in this town (correct answer)
  3. The mean income of $68,000\$68{,}000 is the most accurate representation because it includes all residents and reflects the town's total wealth
  4. The small change in median indicates that income distribution is uniform, making either measure equally appropriate for policy decisions
Explanation: The dramatic decrease in mean ($16,000\$16{,}000) compared to the minimal change in median ($1,000\$1{,}000) when removing the highest earners indicates these are outliers that severely skew the distribution. The median of $48,000\$48{,}000 better represents what a typical resident earns. Choice A is wrong because symmetric distributions would show similar changes in both measures. Choice C confuses total wealth with typical income representation. Choice D incorrectly interprets the small median change as indicating uniform distribution, when it actually shows the median's resistance to outliers.

Question 17

A city planner examining housing prices finds that in Neighborhood A, the mean price exceeds the median by $180,000\$180{,}000, while in Neighborhood B, the mean exceeds the median by only $15,000\$15{,}000. If both neighborhoods have similar numbers of homes, what does this suggest about using median home price for policy decisions?

  1. Median price would be more reliable in Neighborhood A because the large mean-median gap indicates severe outliers that don't represent typical housing costs (correct answer)
  2. Median price would be more reliable in Neighborhood B because the small mean-median gap indicates a more stable and predictable housing market
  3. Mean price should be used in both neighborhoods because it better reflects the total housing wealth and property tax potential for city planning
  4. The choice between mean and median is irrelevant since both neighborhoods show the same pattern of mean exceeding median, indicating similar market conditions
Explanation: The large gap between mean and median in Neighborhood A ($180,000\$180{,}000 vs. $15,000\$15{,}000 in B) indicates the presence of very expensive outlier properties that severely skew the mean upward. For policy decisions about typical housing costs, the median would be more representative of what most residents actually pay. Choice B misses that the question asks about median reliability specifically. Choice C introduces a different consideration (total wealth) rather than addressing typical costs. Choice D incorrectly assumes similar patterns mean similar conditions, ignoring the magnitude difference.

Question 18

An environmental scientist studying pollution levels notices that after removing two extremely high readings suspected to be from equipment malfunctions, the mean pollution level drops from 78 ppm to 52 ppm, while the median changes from 51 ppm to 50 ppm. What does this pattern suggest about the decision to exclude these readings?

  1. The exclusion is statistically justified because the mean and median now converge, indicating a more normal distribution without the equipment errors
  2. The small change in median confirms these were outliers that should be removed, since robust measures like median are unaffected by valid data points
  3. The exclusion is inappropriate because environmental data naturally contains extreme values, and removing them underestimates true pollution variability
  4. The exclusion may be appropriate if the readings were truly equipment malfunctions, but this should be verified through equipment inspection rather than statistical analysis alone (correct answer)
Explanation: When you encounter questions about removing data points from scientific datasets, you need to balance statistical considerations with the scientific context and methodology behind data collection. The dramatic drop in mean (78 to 52 ppm) with minimal median change (51 to 50 ppm) strongly suggests the removed readings were extreme outliers. This pattern indicates the data was highly right-skewed, with the two suspect readings pulling the mean far above the median. Answer D is correct because it recognizes that while the statistical evidence suggests these were likely problematic readings, the decision to exclude data should be based on verified equipment malfunction rather than statistical analysis alone. Scientific integrity requires investigating the actual cause of unusual readings before removal. Answer A incorrectly assumes that convergence of mean and median automatically justifies exclusion. While this suggests the remaining data may be more normally distributed, it doesn't prove the readings were erroneous. Answer B misunderstands robust statistics—medians can still change when removing outliers, and the fact that it changed only slightly doesn't automatically validate the exclusion. Answer C makes a valid point about environmental variability but fails to consider that genuine equipment malfunctions should be removed from datasets intended to measure actual pollution levels. The key distinction is between outliers (extreme but valid data) and erroneous measurements (invalid data due to equipment failure). Statistical patterns can suggest which scenario you're facing, but scientific methodology requires verifying the underlying cause before making exclusion decisions.

Question 19

A teacher analyzes test scores and discovers that one student's score of 95 points is flagged as a potential outlier in a dataset where the mean is 73 and the median is 71. If this score is actually removed, the new mean becomes 71 and the new median becomes 70. What does this suggest about the appropriateness of removing this data point?

  1. The removal is justified because both measures converged closer together, indicating the score was distorting the true center of the distribution
  2. The removal is inappropriate because the score of 95 represents legitimate high performance and removing it understates student achievement in the class (correct answer)
  3. The removal is necessary because outliers always indicate measurement errors, and the resulting mean of 71 now matches typical performance levels
  4. The removal should be based on curriculum standards rather than statistical measures, since both the original and new values fall within acceptable ranges
Explanation: A score of 95 on a test is a legitimate high performance, not an error or invalid data point. While it may be statistically unusual, removing valid data points simply because they're outliers is inappropriate and would misrepresent the actual distribution of student performance. Choice A incorrectly assumes convergence of mean and median always justifies removal. Choice C wrongly assumes outliers always indicate errors. Choice D introduces irrelevant criteria about curriculum standards rather than focusing on the statistical principle of data integrity.

Question 20

Two different news outlets report on the same salary survey. Outlet A reports the mean salary as $85,000\$85{,}000 and recommends using this figure because "it accounts for high earners who drive economic growth." Outlet B reports the median salary as $58,000\$58{,}000 and recommends this figure because "it represents what most workers actually earn." If both statistics are calculated correctly, what can be concluded about the salary distribution?

  1. The distribution is right-skewed with high-earning outliers, and both outlets' reasoning contains some validity depending on the intended purpose of the statistic (correct answer)
  2. The distribution is left-skewed with low-earning outliers, and Outlet A's reasoning is more statistically sound since the mean uses all data points
  3. The distribution is approximately normal since both measures are positive, and the choice between them is purely a matter of personal preference
  4. One of the outlets must have made a calculation error since the mean and median should be nearly equal for any legitimate salary distribution
Explanation: The mean ($85,000\$85{,}000) being substantially higher than the median ($58,000\$58{,}000) indicates a right-skewed distribution with high-earning outliers pulling the mean upward. Both outlets' reasoning has merit: the mean does reflect the impact of high earners, while the median does represent typical worker earnings. The choice depends on the analytical purpose. Choice B incorrectly identifies the skew direction. Choice C wrongly assumes equal measures indicate normality. Choice D incorrectly assumes mean and median should always be similar.