Dot Plots, Histograms, and Box Plots

Data Displays

By the end of this lesson, you will be able to construct and interpret dot plots, stem-and-leaf plots, histograms, and box plots.

Dot Plot

Each data value is represented by a dot above a number line. Works best for small datasets (n ≤ 30).

Example: Test scores: 72, 75, 75, 78, 80, 82, 85, 85, 88, 92

Each value gets a dot; if a value repeats, dots stack vertically.

Reading: look for clusters (where most dots are), gaps, and outliers (dots far from the group).

Stem-and-Leaf Plot

Stem | Leaf
  7  | 2 5 5 8
  8  | 0 2 5 5 8
  9  | 2
Key: 7|2 = 72

The stem is the leading digit(s); the leaf is the last digit. Good for showing the distribution while retaining actual values.

Example (same scores):

Back-to-back stemplot: put leaves for two groups on either side of the stems — great for comparing two datasets.

Histogram

Like a bar chart for quantitative data, but bars touch (no gaps). Groups data into equal-width bins.

Reading a histogram:

• Tallest bar: most frequent range of values
• Shape: symmetric, right-skewed (tail to the right), left-skewed?
• Spread: how wide is the distribution?
• Outliers: isolated bars far from the main body?

Histogram vs. Bar Chart:

• Bar chart: categorical data, bars DON'T touch
• Histogram: quantitative data, bars DO touch

Box Plot (Box-and-Whisker)

Displays the five-number summary: Min, Q₁, Median, Q₃, Max.

Min   Q1         M         Q3   Max
|-----|[=========|==========]-----|

• Box: from Q₁ to Q₃ (the IQR — middle 50% of data)
• Line in box: the median
• Whiskers: extend to min and max (non-outliers)
• outliers