AP Stats Descriptive Statistics 2 — Questions and Answers
Question 1: A dataset has a mean of 50 and a standard deviation of 10. What is the z-score of the value 35?
- -1.5 (Correct answer)
- -2.0
- 1.5
- 2.0
Correct answer: -1.5
z = (35 - 50) / 10 = -15/10 = -1.5.
Question 2: Which measure of spread is most affected by extreme outliers?
- Range (Correct answer)
- Interquartile range
- Standard deviation
- Median absolute deviation
Correct answer: Range
The range uses only the minimum and maximum values, so a single extreme outlier directly changes it.
Question 3: In a right-skewed distribution, which ordering is typically correct?
- Mean > Median > Mode (Correct answer)
- Mode > Median > Mean
- Mean = Median = Mode
- Median > Mean > Mode
Correct answer: Mean > Median > Mode
Right skew pulls the mean toward the tail, so mean exceeds median, which exceeds mode.
Question 4: A five-number summary shows Min=10, Q1=25, Median=40, Q3=55, Max=100. What is the IQR?
- 30 (Correct answer)
- 90
- 15
- 65
Correct answer: 30
IQR = Q3 - Q1 = 55 - 25 = 30.
Question 5: Which graphical display is best for comparing the distribution shapes of two groups side by side?
- Back-to-back stemplot (Correct answer)
- Pie chart
- Bar chart
- Frequency polygon
Correct answer: Back-to-back stemplot
A back-to-back stemplot shares a common stem and shows both distributions' shapes simultaneously.
Question 6: A student scores at the 84th percentile on a standardized test. This means:
- 84% of students scored at or below this student (Correct answer)
- The student answered 84% of questions correctly
- 84% of students scored above this student
- The student scored 84 points
Correct answer: 84% of students scored at or below this student
A percentile indicates the percentage of the distribution at or below the given score.
Question 7: If every value in a dataset is multiplied by 3, what happens to the standard deviation?
- It is multiplied by 3 (Correct answer)
- It is multiplied by 9
- It stays the same
- It is divided by 3
Correct answer: It is multiplied by 3
Multiplying all values by a constant c multiplies the standard deviation by |c|.
AP Stats Descriptive Statistics 2
A dataset has a mean of 50 and a standard deviation of 10.
What is the z-score of the value 35?