Histograms, Frequency Polygons, and Ogives

What is a histogram?  A graphic representation of the frequency distribution of a continuous variable. Rectangles are drawn in such a way that their bases lie on a linear scale representing different intervals, and their heights are proportional to the frequencies of the values within each of the intervals.

Uses for a Histogram A Histogram can be used:  to display large amounts of data values in a relatively simple chart form.  to tell relative frequency of occurrence.  to easily see the distribution of the data.  to see if there is variation in the data.  to make future predictions based on the data.

Definition: Bin  The class size (width of the rectangles) in a histogram

 X-axis: range of data sub-divided into bins  Y-axis: frequency

Quick Review of histogram shapes

The frequency polygon is a graph that displays the data by using lines that connect points plotted for the frequencies at the midpoints of the classes. The frequencies are represented by the heights of the points.

Polygon  Data on the X-axis is the mid-point of each class  Include a class above and below your highest and lowest data points  Should touch x-axis on both sides

Find the midpoints of each class

Create a frequency polygon using the data Class Boundaries Frequency (f)

Create a frequency polygon using the data

Cumulative Frequency Graph (Ogive)   The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

Class Boundaries Frequency (f)

Draw the x and y axis Plot the points

Histogram

Polygon

Ogive