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Quiz: Displaying Quantitative Data

Test your understanding of dotplots, stemplots, histograms, and distribution shapes with these review questions.

1. What is a key feature that distinguishes a histogram from a bar graph?

  1. Histograms display categorical data
  2. Histogram bars touch each other because the variable is continuous
  3. Histograms can only show relative frequencies
  4. Bar graphs always show larger datasets
Show Answer

The correct answer is B. In a histogram, bars touch each other because the quantitative variable is continuous with no gaps between intervals. In a bar graph for categorical data, bars are separated by gaps to emphasize that categories are distinct and not continuous.

Concept Tested: Histogram

2. A stemplot displays the values 4|2 5 8 where the key states "4|2 means 42." What values are represented?

  1. 4, 2, 5, 8
  2. 42, 45, 48
  3. 42, 52, 82
  4. 4.2, 4.5, 4.8
Show Answer

The correct answer is B. In a stemplot, the stem (4) combines with each leaf (2, 5, 8) to form complete values. With the key "4|2 means 42," the stem represents the tens digit and each leaf represents a ones digit, giving us 42, 45, and 48.

Concept Tested: Stemplot

3. A distribution where the left side mirrors the right side is called:

  1. Skewed right
  2. Skewed left
  3. Symmetric
  4. Bimodal
Show Answer

The correct answer is C. A symmetric distribution has left and right sides that are roughly mirror images of each other. If you could fold the histogram down the middle, both sides would match up. Many natural phenomena produce symmetric distributions, including heights and standardized test scores.

Concept Tested: Symmetric Distribution

4. Income distribution in the United States typically has a long tail stretching toward higher values. This distribution is:

  1. Symmetric
  2. Skewed left
  3. Skewed right
  4. Uniform
Show Answer

The correct answer is C. Income is skewed right (positively skewed) because most people earn modest amounts while a small number earn very high incomes, creating a long tail toward the higher values. Remember: the direction of the skew matches where the tail stretches, not where most values are located.

Concept Tested: Skewed Right

5. A histogram of ages at a family reunion shows two distinct peaks: one around age 8 and another around age 45. This distribution is:

  1. Unimodal
  2. Bimodal
  3. Uniform
  4. Skewed right
Show Answer

The correct answer is B. A bimodal distribution has two distinct peaks, often suggesting that the data comes from two different groups. In this case, the peaks likely represent children (around age 8) and their parents (around age 45), with few people in between.

Concept Tested: Bimodal Distribution

6. When choosing bin width for a histogram, what is the main tradeoff?

  1. Wider bins show more detail but hide patterns
  2. Narrower bins may show random noise while wider bins may hide important features
  3. Bin width does not affect how the histogram looks
  4. You should always use exactly 5 bins
Show Answer

The correct answer is B. Choosing bin width involves balancing competing goals. Too narrow bins show too much detail including random noise. Too wide bins lose important features and make everything look too smooth. The best approach is to try several different bin widths to find one that reveals patterns clearly.

Concept Tested: Choosing Bin Width

7. Which display type is best for a small dataset of 15 values when you want to see every individual value?

  1. Histogram with wide bins
  2. Pie chart
  3. Dotplot
  4. Two-way table
Show Answer

The correct answer is C. Dotplots are ideal for small to moderate datasets (usually fewer than 50 observations) when you want to see every individual value. Each observation gets its own dot, so nothing is hidden. For larger datasets, histograms work better as they group values into bins.

Concept Tested: Dotplot

8. A value that falls notably far from the main pattern of the data is called:

  1. A mode
  2. An outlier
  3. A variable
  4. A percentile
Show Answer

The correct answer is B. An outlier is an observation that falls notably far from the main pattern of the data. Outliers can represent genuine unusual cases, measurement errors, or values from a different population. They should be investigated, not automatically removed.

Concept Tested: Outlier

9. What does the acronym SOCS stand for when describing distributions?

  1. Statistics, Observations, Calculations, Summaries
  2. Shape, Outliers, Center, Spread
  3. Symmetric, Ordinal, Categorical, Skewed
  4. Sample, Observation, Correlation, Standard deviation
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The correct answer is B. SOCS stands for Shape, Outliers, Center, and Spread. When describing a distribution, you should address all four components: What shape does it have? Are there outliers? Where is the center? How spread out are the values? Always describe in context using the variable name and units.

Concept Tested: Shape of Distribution

10. A distribution where all values occur with roughly equal frequency is called:

  1. Symmetric
  2. Skewed
  3. Bimodal
  4. Uniform
Show Answer

The correct answer is D. A uniform distribution has no peaks; every value or range of values occurs with roughly equal frequency. Examples include rolling a fair die (each number 1-6 appears equally often) or birthdays throughout the year. The histogram appears flat across all values.

Concept Tested: Uniform Distribution