Overview • What is a Histogram? • What are some possible uses for a Histogram? • Where did the Histogram come from? • How do Histograms work? • A real world example. • An exercise.
What is a Histogram? • A Histogram is a variation of a bar chart in which data values are grouped together and put into different classes. • This grouping allows you see how frequently data in each class occur in the data set.
What is a Histogram (cont.) • Higher bars represent more datavalues in a class. • Lower bars represent fewer datavalues in a class. • On the next slide is an example of what a Histogram looks like.
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.
Where did the Histogram Come From? • The Histogram was first implemented by Kaoru Isikawa, one of Japans’ most renowned experts on quality improvement. • Isikawa spent his life trying to improve quality in Japan.
Where did the Histogram Come From? (cont.) • His major contributions to quality improvement are known as the basic seven tools of quality. • Included in his basic seven tools of quality is the Histogram.
How do Histograms Work? • First, you need need to pick a process to analyze. • Next, you need a large amount of data, at least 100 data values so that patterns can become visible. • Then, you need to assemble a table of the data values that you collected with regards to frequency of data values.
How do Histograms Work? (cont) • Next, you need to calculate some statistics for the Histogram, including: mean, minimum, maximum, standard deviation, class width, number of classes, skewness, and kurtosis. • Then, you actually create the Histogram using these statistics.
How do Histograms Work? (cont) • After you have created a Histogram, it will take one of five shapes: • Normal Distribution:
How do Histograms Work? (cont) • Positively Skewed: • Negatively Skewed:
How do Histograms Work? (cont) • Bi-Modal Distribution: • Multi-Modal Distribution:
How do Histograms Work? (cont) • Once your Histogram is complete, you can analyze its shape, as well as the statistics that you came up with. • This analysis will help you to make better decisions toward quality improvements.
Real World Example • The next slide contains a real world example of a histogram. It plots the relative frequency of the heights of some students based on the data below. Frequency:Height (feet): (Number of pupils) Relative frequency:0-2 0 02-4 1 14-5 4 85-6 8 166-8 2 2
Real World Example • This Histogram is courtesy of http://www.gcsemaths.fsnet.co.uk/page5.html
Exercise • A great exercise which would help you better understand what a histogram is all about can be found at : http://www.usfca.edu/histogram_explorer/he.html Here you are walked through the making of a histogram. You see all of the aspects that I have discussed in this tutorial.
Summary • After going through this tutorial you should have a better idea of: • What a Histogram is. • What a Histogram is used for. • Where the Histogram came from. • How Histograms work.