Common Mistakes: Statistics
Learn
Learning from common mistakes is one of the fastest ways to improve. This lesson identifies the most frequent errors students make in statistics and shows you how to avoid them.
Why Study Mistakes?
- Recognizing errors helps you catch them in your own work
- Understanding why mistakes happen deepens your conceptual knowledge
- SAT and ACT tests often include answer choices based on common errors
- Being aware of pitfalls improves test-taking speed and accuracy
Examples of Common Mistakes
Mistake 1: Forgetting to Order Data Before Finding the Median
Wrong approach: Data: 8, 3, 12, 5, 9. The middle number is 12, so median = 12.
Correct approach: First order: 3, 5, 8, 9, 12. The middle number is 8, so median = 8.
Why it happens: Students try to save time by not ordering, but the median requires ordered data.
Mistake 2: Finding the Median Incorrectly for Even-Numbered Data Sets
Wrong approach: Data: 2, 4, 6, 8. Picking 4 or 6 as the median.
Correct approach: Average the two middle values: (4 + 6) / 2 = 5. Median = 5.
Why it happens: Students forget that even-numbered sets require averaging the two middle values.
Mistake 3: Confusing Mean and Median When Outliers Exist
Problem: Salaries: $40,000, $42,000, $45,000, $48,000, $200,000.
Wrong interpretation: Mean = $75,000, so typical salary is $75,000.
Correct interpretation: Median = $45,000 is a better measure of typical salary because the $200,000 outlier skews the mean.
Why it happens: Students default to using the mean without considering the data distribution.
Mistake 4: Calculating MAD Without Using Absolute Values
Wrong approach: Data: 2, 4, 6. Mean = 4. Deviations: -2, 0, 2. Average: 0.
Correct approach: Use absolute values: |-2| = 2, |0| = 0, |2| = 2. MAD = (2 + 0 + 2) / 3 = 1.33
Why it happens: Students forget that negative and positive deviations would cancel out without absolute values.
Mistake 5: Computing Range as (Max + Min) Instead of (Max - Min)
Wrong approach: Data: 5, 10, 15, 20, 25. Range = 25 + 5 = 30.
Correct approach: Range = 25 - 5 = 20.
Why it happens: Confusion about the definition of range.
Mistake 6: Thinking No Mode Means Mode = 0
Wrong approach: Data: 2, 4, 6, 8. All values appear once, so mode = 0.
Correct approach: When no value repeats, there is no mode (or we say the data set has no mode).
Why it happens: Confusing "no mode" with a numerical value of zero.
Mistake 7: Miscounting Data Points When Finding the Mean
Wrong approach: Data: 10, 20, 30, 40. Sum = 100. Mean = 100 / 5 = 20.
Correct approach: There are 4 values, not 5. Mean = 100 / 4 = 25.
Why it happens: Rushing or miscounting, especially with larger data sets.
Mistake 8: Comparing Variability Without the Same Scale
Wrong approach: Test A range = 20 points (out of 100). Test B range = 15 points (out of 50). Concluding Test B has less variability.
Correct approach: Consider the relative variability. Test A: 20/100 = 20%. Test B: 15/50 = 30%. Test B actually has more relative variability.
Why it happens: Not accounting for different scales or maximum values.
Practice
Each problem contains an error. Find the mistake, explain what went wrong, and calculate the correct answer.
Problem 1: Student's work: "Data: 15, 8, 22, 11, 19. The median is 22 because it's in the middle." Find and correct the error.
Problem 2: Student's work: "Data: 4, 6, 8, 10. The median is 6 because it's close to the middle." Find and correct the error.
Problem 3: Student's work: "To find the range of 12, 18, 25, 30, I calculated 30 + 12 = 42." Find and correct the error.
Problem 4: Student's work: "Data: 5, 5, 10, 15, 20. Mean = (5 + 10 + 15 + 20) / 4 = 12.5." Find and correct the error.
Problem 5: Student's work: "Data: 3, 7, 9, 13. No number repeats, so the mode is 0." Find and correct the error.
Problem 6: Student's work: "Home prices: $150,000, $160,000, $170,000, $180,000, $950,000. The average home price of $322,000 represents a typical home." Explain why this interpretation is problematic.
Problem 7: Student's work: "Data: 10, 14, 18. Mean = 14. Deviations from mean: -4, 0, 4. MAD = (-4 + 0 + 4) / 3 = 0." Find and correct the error.
Problem 8: Student's work: "I need an 85 average on 4 tests. My first 3 scores are 80, 82, 88. So I need (80 + 82 + 88 + x) / 3 = 85." Find and correct the error.
Problem 9: A student says, "The range of Set A is 15 and the range of Set B is 12, so Set B's data is more consistent." What additional information would you need to verify this claim?
Problem 10: Student's work: "Data: 2, 2, 4, 4, 6, 6. The mode is 2 because it's the first number that repeats." Find and correct the error.
Problem 11: A survey found the mean number of pets per household is 2.3. A student says, "Most families have 2.3 pets." Explain why this statement is misleading.
Problem 12: Student's work for finding Q1 of the data 5, 8, 12, 15, 18, 22, 25, 28: "Q1 is the median of the lower half. Lower half: 5, 8, 12, 15. Q1 = 12." Find and correct the error.
Check Your Understanding
Answer these questions to confirm you can spot common errors.
- What must you always do before finding the median?
- How do you handle finding the median when there's an even number of data points?
- Why do we use absolute values when calculating MAD?
- When is the median preferred over the mean?
- What does it mean when a data set has "no mode"?
Next Steps
- Review your past work and look for any of these common mistakes
- Create a personal checklist to verify your statistical calculations
- Take the Unit Quiz to test your complete understanding