Intervals

Definition

Intervals are ranges of values used to group data points in histograms, frequency polygons, and time series graphs. They help simplify complex datasets by categorizing data into manageable segments.

5 Must Know Facts For Your Next Test

1. Intervals must be mutually exclusive and collectively exhaustive to ensure all data points are included without overlap.
2. The choice of interval width can significantly affect the appearance and interpretation of a histogram or frequency polygon.
3. Equal-width intervals are commonly used but sometimes unequal intervals are necessary for better representation of data distribution.
4. In time series graphs, intervals often represent regular time periods such as days, months, or years.
5. Determining the number of intervals can involve using formulas like Sturges' Rule or the square root choice method.

Review Questions

• Why is it important for intervals to be mutually exclusive and collectively exhaustive?
• How does the choice of interval width impact a histogram?
• What are two common methods for determining the number of intervals?

Related terms

Histogram: A graphical representation that organizes a group of data points into user-specified ranges (intervals) showing the frequency distribution.

Frequency Polygon: A line graph that shows the frequencies of different classes (intervals) in a dataset by connecting midpoints at each class level.

Time Series Graph: $A$ plot that shows how a variable changes over specific time intervals, often with consistent spacing between intervals such as daily or yearly.