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Histogram

Page history last edited by David King 11 years, 5 months ago

A Histogram (or relative frequency histogram) uses adjacent bars to show the distribution of a single quantitative variable. Each bar of a histogram represents the frequency (or relative frequency) of values. A bin is an interval in which the data values collected will be placed in to. Bin width determines how large the interval will be, capturing more or less data values depending on the size. It is important to note that an empty bin in a histogram isn't just separating data but it means that data has not been collected and that bin is empty.

 

For example if you are showing the distribution of data on the Richter scale you may have bin widths of .5 or 1. This means that any earthquakes with a magnitude of 0-.5 or 0-1 will be placed into the first bin depending on the width of the bin. When looking at a histogram, the Y axis will show the frequency or relative frequency of that quantitative data showing up. The X axis will show the bins which the data is placed into with appropriate widths.

 

You want the histogram to look good, be easy to read and easy to follow, in order to do that we change the widths of the bins. After binning the data so it is easy to read and interpret we can check normality conditions. The three normality conditions for histograms are for it to be symmetric, unimodal, and without outliers. After conditions are met we can analyze the data. Histograms are good for looking at the spread and distribution of the data visually.

 

For our data we have the sum of points that both teams scored for the first 45 Super Bowl games. We have a single quantitative variable which is the sum of points from both teams for the first 45 years. This data is looking at the total points scored by both teams during the first 45 Super Bowl games. On the x axis is where you will find the bins or intervals, and the y axis is where you can find the frequency of scores within any particular bin. We only have one quantitative variable so that is placed on the x axis.

 

 

First, check the normality conditions. It doesn't contain any outliers, looks to be roughly symmetric, and it appears to be unimodal. It shows us that the most frequent total of points scored during the first 45 super bowl games was between 45 and 50. We had a few games where the total scores were low, they only scored between 20 and 25 points. From the histogram we cans see that in most of the games the points scored were from 35 to 60. We have a bin that is empty and it is from 70 to 75. During one game both teams scored a total of 75-80 points. This histogram displays the frequency of a data value so we can see the specific number of games that fall within any given bin/interval.

 

Generating a Histogram in SPSS

  • Go to "Graphs" in the top menu.
  • Select "Chart Builder". 
  • A box will pop up, click "Don't show this dialog again" and then click "ok". 
  • In the "Choose From" Menu select histogram. Select the first option which is a simple histogram.
  • Click and drag histogram to preview window.
  • Drag the quantitative data on the X axis.
  • Click "ok".
  • The histogram is now displayed in the output window.

 

Changing Bin Width in SPSS

  • In the output window of SPSS, double click the histogram to view chart editor.
  • Double click bars to open the chart editor.
  • Click on the binning tab.
  • Select "Interval Width" in the x-axis section. 
  • Enter desired bin width.

          Or

  • Select "number of intervals" and enter the amount of bins you would like to have. 

 

Here's a video that demonstrates how to make a histogram using SPSS:

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