Two Qualitative Variables

Two-Way Frequency Table:

Looks at the relationship between two category variables using rows and columns.

Why can raw frequency graphs be biased?

They mislead if the compared groups have different total sizes.

How do you fix group size bias?

Use relative frequencies (proportions) instead of raw counts.

Dot plot

Best for discrete data with few numbers. Every data point gets its own dot.

Histogram

Best for continuous data or discrete variables with many values. It groups data into blocks called bins.

Box Plot

A visual display used to represent quantitative data that explicitly reveals the median of the dataset in its central box.

Histogram vs. Bar Graph

Histograms show number intervals on the bottom; bar graphs show categories.

Skewed Left

The peak is on the right. The long tail points left.

Skewed Right

The peak is on the left. The long tail points right.

Symmetric

The peak is right in the middle. Both sides look balanced.

Multimodal

Has multiple peaks across the chart.

Uniform

Completely flat. All values have the same height.

Bin Width

The size/range of a single bar on a histogram (Calculated by taking the upper limit minus the lower limit of a single bar EX:20−15= 5years).

Lower Limit vs. Upper Limit

Lower: The smallest data value that can fit into a specific histogram bin (the left edge of the bar).

Upper: The highest data value that can fit into that bin (the right edge of the bar).

Outlier

A data point that sits far away and isolated from the rest of the main distribution structure.