Cheatsheet: Displaying A Single Quantitative Variable

1. Dotplots

1.1 Definition and Construction

1.2 Characteristics

• Best for small to moderate datasets (fewer than 50 values)
• Shows individual data points
• Reveals shape, center, spread, and outliers
• Easy to construct by hand

2. Stemplots (Stem-and-Leaf Plots)

2.1 Definition and Construction

2.2 Construction Steps

1. Separate each observation into a stem and leaf
2. Write stems in a vertical column with smallest at top
3. Write each leaf in the row to the right of its stem
4. Arrange leaves in increasing order from left to right
5. Provide a key

2.3 Splitting Stems

2.4 Back-to-Back Stemplot

• Used to compare two distributions
• Common stem in the middle, leaves for one dataset extend left, leaves for other dataset extend right
• Leaves on left side ordered from right to left (largest closest to stem)

2.5 Characteristics

• Retains original data values
• Best for small to moderate datasets
• Shows shape, center, spread, and outliers
• Can order data as you create the plot

3. Histograms

3.1 Definition and Construction

3.2 Construction Steps

1. Divide the range of data into equal-width classes
2. Count the number of observations in each class
3. Draw bars with heights equal to frequency (or relative frequency)
4. Label axes clearly with variable name and units
5. Bars should touch (no gaps between bars)

3.3 Important Features

3.4 Choosing Number of Classes

• Too few classes: lose detail, distribution appears blocky
• Too many classes: too much detail, distribution appears jagged
• Common practice: use 5-20 classes depending on dataset size
• Choose class width that creates convenient intervals

3.5 Characteristics

• Best for large datasets
• Individual data values are not visible
• Shows shape, center, spread, and outliers of distribution
• Shape depends on number and width of classes chosen

4. Describing Distribution Shape

4.1 Symmetry and Skewness

4.2 Modality

4.3 Other Shape Characteristics

• Bell-shaped: symmetric and unimodal, resembles a bell curve
• Gaps: spaces in the distribution where no data values occur
• Clusters: groups of data separated by gaps

5. Describing Center, Spread, and Outliers

5.1 Center

• The value around which the data are balanced
• Described by median or mean (specific values calculated separately)
• Estimated visually as the midpoint of the distribution

5.2 Spread (Variability)

• How much the data values vary from each other
• Described by range, IQR, or standard deviation (specific values calculated separately)
• Estimated visually by observing how far data extend from the center

5.3 Outliers

6. Describing Distributions: SOCS

6.1 Complete Description Framework

6.2 Context Requirement

• Always describe distributions in context of the data
• Include variable name and units in descriptions
• Use specific values when possible rather than vague terms

7. Comparing Graphs

7.1 When to Use Each Display

7.2 Advantages and Disadvantages

8. Common Errors to Avoid

8.1 Construction Errors

• Histogram: using unequal class widths (creates misleading bars)
• Histogram: leaving gaps between bars (appropriate only for categorical data)
• Stemplot: forgetting to include a key
• Stemplot: not ordering leaves from smallest to largest
• All graphs: failing to label axes with variable name and units

8.2 Interpretation Errors

• Describing distributions without using context
• Confusing skewness direction (remember: skew direction refers to the longer tail)
• Failing to mention outliers when present
• Being too vague (use specific values and descriptions)