AP Stats Data Visualization and Interpretation 3 — Questions and Answers
Question 1: A histogram of household incomes is strongly right-skewed. Which measure of center best describes the typical household income?
- Mean, because it uses all data values.
- Median, because it is resistant to extreme values. (Correct answer)
- Mode, because it is the most common income.
- Range, because it captures the spread.
Correct answer: Median, because it is resistant to extreme values.
The median is resistant to the extreme high values that pull the mean upward in right-skewed distributions.
Question 2: In a scatterplot, a cluster of points forms a pattern that curves upward and then levels off. The relationship between x and y is best described as:
- Linear and positive.
- Linear and negative.
- Non-linear. (Correct answer)
- There is no association.
Correct answer: Non-linear.
A curved (not straight-line) pattern in a scatterplot indicates a non-linear relationship.
Question 3: A stemplot of exam scores has stems 5, 6, 7, 8, 9 with stem 7 having the most leaves. This indicates that the distribution is:
- Right-skewed with center around 90.
- Roughly symmetric or unimodal with center near 70. (Correct answer)
- Bimodal with peaks at 50 and 90.
- Uniform across all score ranges.
Correct answer: Roughly symmetric or unimodal with center near 70.
The stem with the most leaves represents the most common values, placing the center of the distribution near 70.
Question 4: Which of the following best describes the purpose of a residual plot in regression analysis?
- To display the raw data values plotted against each other.
- To check whether a linear model is appropriate for the data. (Correct answer)
- To calculate the correlation coefficient.
- To identify the y-intercept of the regression line.
Correct answer: To check whether a linear model is appropriate for the data.
A residual plot showing random scatter around zero supports a linear model; patterns suggest non-linearity.
Question 5: A pie chart shows that 40% of survey respondents prefer Brand A, 35% prefer Brand B, and 25% prefer Brand C. Which limitation does this pie chart have compared to a bar chart?
- Pie charts cannot show more than two categories.
- Pie charts make it harder to compare similar-sized slices precisely. (Correct answer)
- Pie charts cannot represent percentages.
- Pie charts require interval-level data.
Correct answer: Pie charts make it harder to compare similar-sized slices precisely.
Humans have difficulty judging angles and areas accurately, making precise comparisons between similar-sized pie slices difficult.
Question 6: A side-by-side boxplot compares the salaries of employees in two departments. Department X has a larger IQR than Department Y. This means:
- Department X has more employees.
- The middle 50% of salaries in Department X is more spread out. (Correct answer)
- Department X has a higher median salary.
- Department X has more outliers.
Correct answer: The middle 50% of salaries in Department X is more spread out.
The IQR (Q3 − Q1) measures the spread of the middle 50% of data, so a larger IQR indicates more variability in that range.
Question 7: When constructing a frequency histogram, increasing the number of bins (class intervals) will generally:
- Always make the distribution appear more symmetric.
- Show more detail but may create erratic patterns with small samples. (Correct answer)
- Reduce the total area under the histogram.
- Make outliers disappear.
Correct answer: Show more detail but may create erratic patterns with small samples.
More bins reveal finer detail but with small datasets can create irregular patterns that obscure the overall shape.
AP Stats Data Visualization and Interpretation 3
A histogram of household incomes is strongly right-skewed.
Which measure of center best describes the typical household income?