Stemplot (Stem-and-Leaf Plot):

$\text{Stem} | \text{Leaf}$ $0 | \text{(no leaves — no scores in 0-9 range except...)}$ $\text{or start at 8:}$ $8 | \text{ }$ $9 | 0 \; 0$ $10 | 0 \; 0 \; 0$ $11 | 0$ $12 | 0 \; 0$ $13 | 0$

Wait, let me recalculate. Scores are: 8, 9, 9, 10, 10, 10, 11, 12, 12, 13

Better notation:

• 8 = stem 0, leaf 8 (or stem 8, leaf nothing)
• 9, 9 = stem 0, leaves 9, 9
• 10, 10, 10 = stem 1, leaves 0, 0, 0
• etc.

$\text{Stem} | \text{Leaf}$ $0 | 8 \; 9 \; 9$ $1 | 0 \; 0 \; 0 \; 1 \; 2 \; 2 \; 3$

Or in traditional format: $8 | \text{ }$ $9 | 0 \; 0$ $10 | 0 \; 0 \; 0$ $11 | 0$ $12 | 0 \; 0$ $13 | 0$

Interpretation: Most scores cluster at 10; shape is roughly symmetric with a slight left skew (tail toward lower scores). No outliers.

Dotplot: When to use

• Small datasets (roughly < 20–30 values)
• You want to see each individual point
• Data is discrete or you want to preserve exact values
• Patterns and clusters matter more than overall frequency

Example: 10 students' test scores: 78, 82, 82, 85, 88, 90, 90, 92, 95, 98

Each dot placed above a number line shows exact scores, and you can see two students scored 82, two scored 90, etc.

Histogram: When to use

• Large datasets (typically 30+ values)
• Data is continuous or has many distinct values
• You're interested in overall shape and frequency distribution, not individual points
• You want to group values into intervals (bins)

Example: Heights of 200 students

Instead of 200 individual dots, group heights into bins: 60–62", 62–64", 64–66", etc. Bars show how many students fall in each interval. The shape (symmetric, skewed, etc.) emerges clearly.

Key difference: Dotplots show individual data; histograms show distribution shape and patterns across groups.

Histogram:

• Reveals: Full shape (symmetric, skewed, bimodal), exact frequency in each bin, where most data concentrates
• Best for: Overall distribution pattern
• Drawback: Bin width choice can mislead; loses individual data points

Boxplot:

• Reveals: Five-number summary (min, Q1, median, Q3, max), IQR (spread of middle 50%), identification of outliers, left/right skew
• Best for: Quick comparison of center and spread; identifying outliers
• Drawback: Hides the shape details (can't see if bimodal); loses frequency info

Dotplot:

• Reveals: Each exact data point, clustering, individual values
• Best for: Small datasets or when precision matters
• Drawback: With 500 points, it becomes unreadable — visual overload; impossible to see patterns

Recommendation for 500 values:

1. Primary: Histogram for overall shape and distribution
2. Secondary: Add boxplot alongside to highlight outliers and quartiles
3. Skip dotplot — too many points obscure the view

This combination gives complete picture: shape (histogram) + resistant summary (boxplot).