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Chapter 4

Frequency Distributions

Book Version 1
By Boundless
Boundless Statistics
Statistics
by Boundless
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Section 1
Frequency Distributions for Quantitative Data
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Guidelines for Plotting Frequency Distributions

The frequency distribution of events is the number of times each event occurred in an experiment or study.

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Outliers

In statistics, an outlier is an observation that is numerically distant from the rest of the data.

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Relative Frequency Distributions

A relative frequency is the fraction or proportion of times a value occurs in a data set.

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Cumulative Frequency Distributions

A cumulative frequency distribution displays a running total of all the preceding frequencies in a frequency distribution.

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Graphs for Quantitative Data

A plot is a graphical technique for representing a data set, usually as a graph showing the relationship between two or more variables.

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Typical Shapes

Distributions can be symmetrical or asymmetrical depending on how the data falls.

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Z-Scores and Location in a Distribution

A $z$-score is the signed number of standard deviations an observation is above the mean of a distribution.

Section 2
Frequency Distributions for Qualitative Data
Describing Qualitative Data

Qualitative data is a categorical measurement expressed not in terms of numbers, but rather by means of a natural language description.

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Interpreting Distributions Constructed by Others

Graphs of distributions created by others can be misleading, either intentionally or unintentionally.

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Graphs of Qualitative Data

Qualitative data can be graphed in various ways, including using pie charts and bar charts.

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Misleading Graphs

A misleading graph misrepresents data and may result in incorrectly derived conclusions.

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Do It Yourself: Plotting Qualitative Frequency Distributions

Qualitative frequency distributions can be displayed in bar charts, Pareto charts, and pie charts.

Summation Notation

In statistical formulas that involve summing numbers, the Greek letter sigma is used as the summation notation.

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Graphing Bivariate Relationships

We can learn much more by displaying bivariate data in a graphical form that maintains the pairing of variables.

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Boundless Statistics by Boundless
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Visualizing Data
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Frequency Distributions
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