Histograms, Frequency Histograms, Frequency Polygons, and OgivesPolygons, and Ogives

What is a histogram?What is a histogram?

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

Uses for a Histogram Uses for a Histogram

A Histogram can be used:A Histogram can be used: to display large amounts of data values to display large amounts of data values

in a relatively simple chart form.in a relatively simple chart form. to tell relative frequency of occurrence.to tell relative frequency of occurrence. to easily see the distribution of the data.to easily see the distribution of the data. to see if there is variation in the data.to see if there is variation in the data. to make future predictions based on the to make future predictions based on the

data. data.

Definition: BinDefinition: Bin

The class size (width of the The class size (width of the rectangles) in a histogramrectangles) in a histogram

X-axis: range of data sub-divided X-axis: range of data sub-divided into binsinto bins

Y-axis: frequencyY-axis: frequency

Quick Review of histogram shapesQuick Review of histogram shapes

The frequency polygon is a graph that displays the data by using lines

that connect points plottedfor the frequencies at the midpoints of the classes. The frequencies are

represented by the heightsof the points.

Find the midpoints of each classFind the midpoints of each class

Find the midpoints of each classFind the midpoints of each class

Create a frequency polygon using Create a frequency polygon using the datathe data

Create a frequency polygon using Create a frequency polygon using the datathe data

Cumulative Frequency GraphCumulative Frequency Graph(Ogive)(Ogive)

The ogive is a graph that represents the cumulative frequencies for the classes in a frequency distribution.

Create an ogiveCreate an ogive

Draw the x and y axisDraw the x and y axis

Plot the pointsPlot the points

AssignmentAssignment

Read through example 2-7 on page Read through example 2-7 on page 5454

Do Exercise Set 2-3 1-14 on page 57Do Exercise Set 2-3 1-14 on page 57