Common Mistakes
Learning Objectives
In this lesson, you will:
- Identify frequent errors in statistical calculations
- Understand misconceptions about data interpretation
- Learn strategies to avoid common pitfalls
- Build accuracy through error awareness
Practice Quiz
Identify the error and find the correct answer. Click each question to reveal the solution.
Question 1: A student says the median of 3, 7, 9, 12 is 8. What is the error?
Error: Forgetting to average the two middle values for an even-numbered data set.
Correct: Median = (7 + 9) / 2 = 8. Actually, the student got the right answer but should show the work: with 4 values, average the 2nd and 3rd.
Question 2: A student calculates range as "maximum + minimum" instead of "maximum - minimum." For data 5, 8, 12, what is the correct range?
Error: Range is the difference, not the sum.
Correct: Range = 12 - 5 = 7 (not 12 + 5 = 17).
Question 3: A student says a data set with no repeated values has "no mode." Is this correct?
Answer: Yes, this is correct.
Explanation: If no value appears more than once, the data set has no mode (or some say it's undefined). This is not an error.
Question 4: A student forgets to order data before finding the median. For 8, 3, 10, 5, 7, they take the middle value as 10. What is the correct median?
Error: Data must be ordered first.
Correct: Ordered: 3, 5, 7, 8, 10. Median = 7 (the 3rd of 5 values).
Question 5: A student confuses IQR with range. For Q1 = 20 and Q3 = 45 with min = 10 and max = 60, what is the IQR?
Error: Using min and max instead of Q1 and Q3.
Correct: IQR = Q3 - Q1 = 45 - 20 = 25. (Range would be 60 - 10 = 50.)
Question 6: A student says "68% of data is within 1 standard deviation" applies to all data sets. Why is this incorrect?
Error: The 68-95-99.7 rule only applies to normal distributions.
Correct: For skewed or non-normal data, the percentages can be very different. Always check if data is approximately normal before applying this rule.
Question 7: A student claims that if the mean increases, the standard deviation must also increase. Is this true?
Answer: False.
Explanation: Adding the same constant to all values increases the mean but doesn't change the standard deviation. Standard deviation measures spread, not center.
Question 8: A student says an outlier is any value larger than Q3. What is the correct definition?
Error: Incomplete definition of outlier.
Correct: Using the 1.5 IQR rule, outliers are values below Q1 - 1.5(IQR) or above Q3 + 1.5(IQR). Simply being above Q3 doesn't make a value an outlier.
Question 9: A student calculates the mean of 2, 4, 6 as (2 + 4 + 6) / 2 = 6. What is the error?
Error: Dividing by 2 instead of by the count of values (3).
Correct: Mean = (2 + 4 + 6) / 3 = 12 / 3 = 4.
Question 10: A student says correlation implies causation. A study shows ice cream sales and drowning rates are correlated. Does ice cream cause drowning?
Answer: No, correlation does not imply causation.
Explanation: Both variables are influenced by a third factor (hot weather). People swim more AND buy more ice cream when it's hot. This is a lurking variable, not a causal relationship.
Next Steps
- Review each mistake type and practice avoiding it
- Double-check your work on statistics problems
- Take the unit quiz when ready