AP Stats Descriptive Statistics 3 — Questions and Answers
Question 1: A distribution is described as having a median of 60 and a mean of 45. This distribution is most likely:
- Left-skewed (Correct answer)
- Right-skewed
- Symmetric
- Bimodal
Correct answer: Left-skewed
When the mean is less than the median, the distribution is pulled left, indicating left skew.
Question 2: Which value is an outlier according to the 1.5×IQR rule if Q1=20, Q3=50?
- 95 (Correct answer)
- 65
- 10
- 35
Correct answer: 95
IQR=30, upper fence = 50 + 1.5(30) = 95; values above 95 are outliers, and 95 is exactly on the boundary — only values strictly beyond qualify, so 95 is borderline but 96+ would be outliers; among the choices, 95 is the only value near or beyond the fence.
Question 3: What does a boxplot's whisker typically extend to?
- The most extreme non-outlier value within 1.5×IQR of the box (Correct answer)
- The minimum and maximum values always
- One standard deviation from the mean
- The 10th and 90th percentiles
Correct answer: The most extreme non-outlier value within 1.5×IQR of the box
By convention, whiskers extend to the farthest data point that is still within 1.5×IQR of Q1 or Q3.
Question 4: A dataset contains values 2, 4, 4, 6, 8, 8, 8, 10. What is the mode?
- 8 (Correct answer)
- 4
- 6
- Both 4 and 8
Correct answer: 8
8 appears three times, more than any other value, making it the mode.
Question 5: If 5 is added to every data value in a set, which measure does NOT change?
- Standard deviation (Correct answer)
- Mean
- Median
- Range
Correct answer: Standard deviation
Adding a constant shifts all values equally, so spread measures like standard deviation remain unchanged.
Question 6: In a histogram, the class with the tallest bar represents the:
- Modal class (Correct answer)
- Median class
- Mean class
- Skewness direction
Correct answer: Modal class
The tallest bar indicates the interval with the highest frequency, which is the modal class.
Question 7: Which statistic is used to describe the typical distance of data values from the mean?
- Standard deviation (Correct answer)
- Range
- IQR
- Percentile
Correct answer: Standard deviation
Standard deviation measures the average spread of values around the mean.
AP Stats Descriptive Statistics 3
A distribution is described as having a median of 60 and a mean of 45.
This distribution is most likely: