AP Stats Descriptive Statistics 1 — Questions and Answers
Question 1: What is the difference between the mean and the median?
- The mean is the arithmetic average; the median is the middle value when data is ordered (Correct answer)
- They always produce the same result
- The mean is always larger than the median
- The median is calculated by adding all values
Correct answer: The mean is the arithmetic average; the median is the middle value when data is ordered
The mean sums all values and divides by count, while the median identifies the middle value in an ordered dataset.
Question 2: What does standard deviation measure?
- The average amount of variability or spread in a dataset (Correct answer)
- The center of the data distribution
- The highest value in the dataset
- The number of data points
Correct answer: The average amount of variability or spread in a dataset
Standard deviation quantifies how spread out data values are from the mean, indicating the typical distance from the average.
Question 3: When is the median preferred over the mean?
- When the data contains outliers or is heavily skewed (Correct answer)
- When all data values are identical
- When working with nominal data
- When the sample size is very large
Correct answer: When the data contains outliers or is heavily skewed
The median is resistant to extreme values and better represents the center of skewed distributions.
Question 4: What is a frequency distribution?
- A table or graph showing how often each value or range of values occurs (Correct answer)
- A measure of central tendency
- A method for calculating standard deviation
- A type of probability calculation
Correct answer: A table or graph showing how often each value or range of values occurs
A frequency distribution organizes data by showing the count or proportion of observations for each value or interval.
Question 5: What does a box plot display?
- The minimum, first quartile, median, third quartile, and maximum of a dataset (Correct answer)
- Only the mean and standard deviation
- The frequency of each data value
- The correlation between two variables
Correct answer: The minimum, first quartile, median, third quartile, and maximum of a dataset
Box plots provide a visual summary of the five-number summary, showing the distribution, spread, and potential outliers.
Question 6: What is the mode of a dataset?
- The value that appears most frequently (Correct answer)
- The average of all values
- The middle value
- The range of the data
Correct answer: The value that appears most frequently
The mode is the most frequently occurring value in a dataset, and a dataset can have multiple modes or none.
AP Stats Descriptive Statistics 1
What is the difference between the mean and the median?