Constructing and Interpreting a Relative Cumulative Frequency Graph (Ogive)

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1. Overview
A cumulative relative frequency graph serves as a graphically representation of the cumulative relative frequency distribution for quantitative variables. Given a percentile of interest, they can be used to estimate the value of your dataset associated with that percentile.

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2. Constructing a Cumulative Frequency Graph (Ogive)

EXAMPLE 1:
The following data represents Miles Per Gallon (city) estimates for cars selected at random from among 1993 passenger car models that were listed in both the Consumer Reports issue and the PACE Buying Guide. The data was obtained from the Cars93 dataset. With the provided dataset, construct a relative cumulative frequency graph.

Solution: 

Part II - Construct Graph

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3. Determining Percentiles Using Cumulative Frequency Graphs

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4. Comparison Between Histograms and Relative Cumulative Frequency Graphs

There is a direct association between the slope of the Cumulative Frequency Graph for certain intervals and the corresponding frequency count in the same interval of the associated histogram. Notice in Example Two (below) that slope between 2 and 4 is 0, and that the frequency count is also 0 for this section of the histogram. Likewise, between interval 14-16, the slope is greatest in the Relative Cumulative Frequency Graph, while the frequency count during this interval is also the greatest among the other bins.

Example 1

Example 2