Unit 2 Section 2.1 – Day 2

2.1: Frequency Distributions and Their Graph  Graphs are used to present data after it has been organized into frequency distributions.  The purpose of a graphs in statistics is to display data in pictorial form.  The three most commonly used graphs are:  Frequency Histograms  Frequency Polygons  Ogives (pronounced: o-jive)

The Frequency Histogram  Frequency Histogram – a bar graph that represents the frequency distribution of a data set.  The horizontal scale is quantitative and measures the data entries.  The vertical scale measures the frequencies of the class.  Consecutive bars must touch.  Bars begin and end at class boundaries. Section 2.1

How to Construct a Frequency Histogram  Draw and label the x and y axis  Remember x is the horizontal axis and y is the vertical.  Represent the frequency on the y axis and the class boundaries on the x axis.  Using the frequency as the heights, draw vertical bars for each class. Section 2.1

Activity: Construct a Histogram  Using the data on the following slide, construct a histogram to represent the data. Section 2.1

Class Limit Class BoundaryFrequency Section 2.1

The Frequency Polygon  Frequency Polygon – a graph that displays 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. Section 2.1

How to Construct a Frequency Polygon  Find the midpoints of each class.  Add the upper and lower boundary, then divide by 2.  Draw and label the x and y axis  Label the x-axis with the midpoint of each class.  Determine a suitable scale for the frequencies.  Using the midpoints for the x values and the frequencies as the y values, plot the points.  Connect the adjacent points with line segments.  Draw a line back to the x axis at the beginning and end of the graph.  The line should connect at the same distance where the previous and next midpoint would be located. Section 2.1

Activity: Construct a Frequency Polygon  Using the data representing record high data for the 50 states, construct a frequency polygon to represent the data. Section 2.1

The Ogive  Ogive – a graph that represents the cumulative frequencies for the classes in a frequency distribution.  Also known as a cumulative frequency graph. Section 2-3

How to Construct an Ogive  Find the cumulative frequency of each class.  Draw and label the x and y axis  Label the x-axis with the class boundaries of each class.  Determine a suitable scale for the frequencies.  Plot the cumulative frequency at each upper class boundary.  Starting with the first upper class boundary, connect adjacent points. Then extend the graph to the first lower class boundary on the x axis. Section 2.1

Activity: Construct an Ogive  Using the data representing record high data for the 50 states, construct an Ogive to represent the data. Section 2.1

Relative Frequency Histogram  Relative Frequency Histogram – a graph that coverts the distributions from frequencies to proportions of frequencies.  To covert, divide the frequency by the overall cumulative frequency.  The sum of the relative frequencies will always equal 1. Section 2.1

 Pg. 116 – 117 (1 – 11 ODD) Homework