Posts Tagged ‘Creative Thinking’

How to build a good Histogram

Monday, February 20th, 2012

A histogram, one of the Seven Basic QC Tools,  is a very good tool to use to picture what a set of data looks like.  It give shape to a set of data by grouping the data into “cells.” It shows you the spread or dispersion and the central tendency which can be used to compare to a standard or another group of data. In this way it can be an excellent troubleshooting tool by using it to compare different suppliers, equipment, processes to reveal their differences or similarities.

Although most statistical or spreadsheet software can create a histogram for you very easily I am going to talk you through how to create a good histogram by hand. The real key to a good histogram is to get the correct number of “cells” for the size of the set of data you have. If you have to few or to many it will not give you much of a feel for the spread or center of the data you have. Too few looks like a big clump and too many looks like a broad scatter of points. Neither shows or tells you much about your data. So here is what you do to build a histogram by hand.

  1. Find your largest and smallest number in the data and calculate the data range by subtracting the smallest value from the largest one.
  2. Now we determine the all important number of cells for our histogram. These cells will be the columns you see in a histogram. The “Six Sigma Handbook” by Thomas Pyzdek shows two ways to get the correct number of cells for you data. This first number will change a bit as you do some calculations but they are a very good starting point. The first is to use the table below.

Sample Size

Number of Cells

100 or less

7 to 10


11 to 15

201 or more

13 to 20


The second method, using a calculator, you can take the square root of the sample size and round that number to the nearest integer.

  1. Next we determine the width of each cell by dividing the range that you found in the step 1 by the number of cells we determined in step 2.


Once you have calculated the cell width round it to a convenient number. Doing this will affect the number of cells in your histogram, but that will be ok.

  1. Next we will computer the “cell boundaries.” Look at a cell as a range of values of your data. The cell boundaries define the start and end point for each cell in your histogram. Since it will be these start and end point we will make them one more decimal place more than our data values.  Thus if our data values are integers (1, 12, 36)  then our cell boundaries will be one decimal place (xx.x).
  2. Now we determine the low boundary of the first cell. This boundary has to be set less than the smallest value of your data set.
  3. Now that the lowest cell boundary is determined all the other cell boundaries are determined by adding the cell width to the previous boundary. Continue this until the upper boundary  is larger than the largest value in the data set.
  4. Now go through the data that you have and determine in what cell each value goes and make a tick mark in that cell (bounded by the boundaries you calculated).
  5. Count the ticks in each cell and record the total count in each cell.
  6. Now we have all the statistics to create the histogram. First, on graph paper, draw a horizontal line near the bottom of the page. Leave room below to label the cell boundaries on this line.
  7. Starting with the lowest cell boundary, equally space all the boundaries along this line.
  8. Next at the left end of the horizontal line draw a vertical line. This lines length will be just longer than the largest cell count that you found. This line should be label from 0 to the largest cell count or just beyond. This is the count or frequency axis
  9. Last you draw in the columns (or bars) for each of the cells up to the count/frequency of that cell .


So below is a histogram made in Minitab but let me give you the basic information about its data.

    • Lowest Value = 596.2
    • Highest Value = 604.2
    • Range = 8.0
    • There are 200 values in this set of data



Now, let’s see how close it is to the manual method.

  1. Number of cells: Table value 15; Square root method 14.142
  2. Cell Width: Table: 8/15 = .5333 ~  .5 Square Root: 8/14.142 = .5656 ~ .5
  3. lowest Cell Boundary < 596.2  (and one decimal more) = 596.15
  4. All the other boundaries (Largest must be larger than the highest value [604.2]


# Cells Lower Boundary Cell Center Upper Boundary Lowest Val=






Cell Width=

















































































Highest Val=



Well there you have how to build a histogram by hand. . If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt


Understanding Variation

Tuesday, September 28th, 2010

There is variation everywhere. Look around there are no true clones of anything, everything is at least slightly different. Even in identical twins there is a difference that the parents can see to tell them apart. It is variation in the world that feeds evolution. It is this variation that allows life to survive on this planet. Not everything survives but those that adapt (change/ vary) to the changing world do survive. So as a society we tend to classify things at any given moment. Classification gives us an ability to take a look at things and figure out what makes them “tick” (survive). These classification come in one of two types. Those two types are categorical (discrete) information (data) and numerical (continuous) information (data).

Variation Classifications:

Let’s take a good look at these two types of classification of information I call data. First there is Categorical (discrete) data.


Categorical – Belonging to a category.

Categorize – To describe by labeling or giving a name to a group of characteristics.

Discrete – Apart or detached from others; separate; distinct.

Categorical data can only be one of a limited number of non-numerical choices. It is sometimes, in numerical terms (becomes numerical data), called count data because the only way to measure it is by counting. Examples of this type of data are:

  • Best/better/worse
  • Small/Medium/Large
  • Restaurant $$ ratings
  • Movie ** ratings
  • Pass/Fail
  • Yes/No
  • Red cars
  • Doctors
  • Broken
  • Repaired

Second is Numerical ( continuous) data.


Numerical – of  or pertaining to numbers; of the nature of a number.

Continuous – uninterrupted in time; without cessation.

Numerical data is from a measuring process. Examples of this type of data are:

  • Height
  • Weight
  • Length
  • Depth
  • Voltage
  • Time

Business and Variation:

In businesses we compensate for variation to try to meet customer needs and expectations. This compensation cost money. In Six Sigma we try to understand and deal with this variation. We use statistics to help recognize and thus assess the variation by organizing it in a meaningful way. Statistics help change assumptions to conclusions about where the errors (variations) are and how bad it is affecting our business. Statistics help “Picture” the variation we feel or think is happening.


Statistic – a numerical fact usually computed from a sample.

Well there you have my thoughts on understanding variation. Next time I am going to discuss measuring that variation and the proper scale of measurement to use depending on the type of  variation you are trying to measure. If, you have questions or comments please feel free to contact me by leaving a comment below, emailing me, calling me, or leaving a comment on my website.

Bersbach Consulting
Peter Bersbach
Six Sigma Master Black Belt

LCS a Creative Thinking Tool and More

Monday, January 4th, 2010

Creative ThinkingHere is a tool that I feel is the greatest tool for coming up with good creative ideas. Ideas on what happened. Ideas on how it happened. Ideas on what caused it. Ideas on how to fix it. Ideas on how to improve it.

Many times we are in meetings where discussions are taking place and you try to add to the discussion only to have someone else ”Knicks” your comments. The person “Knicking” really did not mean to make it sound like your idea was bad but that is the way it came across. Unusually, you will not add more to the conversation. Once put off we tend to keep quite. Plus, I might add, the issue being discussed never really gets resolved by the group. What is happening here is just something that our culture seems to thrive on and that is negative comments. We tend to always come up with why something will not work. We seem to be focused on that. But we never or rarely come up with why something will work, or at least what is good about that idea.

This tool helps in this discussion area to bring out what is good ( the golden nuggets) first and then discuss the issues with the idea next. So here it the tool:


LCS stands for Likes, Concerns Suggestions. In almost any meeting you can use this tool and you will be amazed at how it improves the discussions in the meeting. Here is how it works:

  1. Everyone in the room must use LCS. At first this means that you will have to explain it to those in the room. Many times I’ll have soft spongy toy’s around the room so if someone does not follow these rules that anyone in the room can and will throw a toy at them to remind them to use LCS.
  2. LIKES – First, if you are going to make a comment about something the first thing you should say about it, is what you like. In doing this you show the person that made the statement and the rest of the members in the room that you understood what was said by identifying things in the statement that you liked. What I call the “Golden Nuggets” of an idea.
  3. CONCERNS – Second, no idea (or comment) is perfect so many times we have some concerns about some points in the original statement. Well those get stated next, but only if you have suggestions to improve or correct your concerns. If you can not come up with a suggested improvement then DO NOT STATE YOUR CONCERN. Why? Because you have no idea that is better. If you did you could add it as a suggestion, which means that you could now state your concern and suggestion for improving it.
  4. SUGGESTIONS –Third, if you state a concern YOU MUST ALWAYS give a suggestion to improve on your concerns. In brainstorming this is called piggybacking off someone else’s idea. They had an idea you liked some of it you had some concerns and suggestions that made the idea better.

Usually the ideas created using LCS are far superior to those that don’t. The reason for that is it is additive intelligence. With a good cross-functional team using LCS a diverse amount of intelligence is brought to the meeting and through LCS it is unleashed to solve an issue or problem the team is working on.

Now remember in Six Sigma even this discussion is only an opinion of the team or group. Now you have to go collect data and prove that the opinion is correct.Well give it a try and let me know what you think. Enjoy

Peter Bersbach

Six Sigma Master Black Belt

Bersbach Consulting

From Process to Profits