Section 2.3

Additional Displays of Quantitative Data

Beyond histograms: Learn how to connect data points to visualize trends over time and understand cumulative accumulation using Polygons, Ogives, and Time-Series Plots.

1

Frequency Polygons

Connecting the Dots

A graph that uses points connected by line segments to represent the distribution.

Plot Points: Uses the Class Midpoint (x-axis) and Frequency (y-axis).
Midpoint = (Lower Limit + Upper Limit) / 2
LogicLens: The Anchor Rule

A frequency polygon must describe a closed geometric shape (a polygon). To do this, we must "anchor" the graph to the x-axis by adding a class with 0 frequency at both the beginning and the end of the distribution.

Interactive Frequency Polygon Tool

Enter quantitative data to generate a Frequency Polygon. Notice how the graph starts and ends at zero (anchored) and connects class midpoints.

Try sample:

Enter data values above or select a sample dataset to get started.

2

Ogives (Cumulative Graphs)

The Power of Accumulation

An Ogive (pronounced "oh-jive") is a graph that represents the Cumulative Frequency or Cumulative Relative Frequency.

How to Construct
  • • Plots points using Upper Class Boundaries (x-axis) and Cumulative Frequency (y-axis).
  • • Connect points with straight lines.
  • • Starts at 0 on the y-axis at the lower boundary of the first class.
  • Never slopes downward (data only accumulates!).
LogicLens: Finding Percentiles

Ogives are powerful for answering questions like:
"What score represents the bottom 50% of the class?"

Find 50% on the y-axis (Relative Frequency), trace horizontally to the line, then drop down to read the x-value.

Interactive Ogive (Cumulative Frequency) Tool

Enter data to generate an Ogive. The graph plots Upper Class Boundaries against Cumulative Frequency.

Try sample:

Enter data values above or select a sample dataset to get started.

3

Time-Series Plots

Tracking Over Time

Obtained by plotting the time on the horizontal axis and the variable's value on the vertical axis. Points are connected by line segments.

Key Function

Used primarily to identify trends (long-term movements) and cycles in data over time.

Trend vs. Seasonality

Trend

A long-term upward or downward movement (e.g., Stock market over 10 years).

Seasonality

Regular, repeating cyclic patterns (e.g., Ice cream sales peaking every July).

Example: Upward Trend

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Insight: Despite minor fluctuations (drops in 2017 & 2020), the long-term direction is clearly upward.

Example: Seasonality

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Insight: A predictable cyclic pattern appearing every year. Sales peak in summer (July) and drop in winter.
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