Central Tendency

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Mean Median and Mode in Central Tendency by Walter McIntyre

Before discussing measures of central tendency, a word of caution is necessary. Customers do not feel averages. They feel their specific experience. As a result, while central tendency is an important descriptive statistic, it is often misused. For example, a customer is told that the average delivery time is noon, but his actual delivery time turns out to be 3:00 PM. The customer, in this case, does not experience the average and may feel that he has been lied to.

The central tendency of a data set is a measure of the predictable center of a distribution of data. Stated another way, it is the location of the bulk of the observations in a data set. Knowing the central tendency of a process’ outputs, in combination with its standard deviation, will allow the prediction of the process’ future performance. The common measures of central tendency are the mean, the median, and the mode. Which of these descriptive statistics you need to use depends on the characteristics of the data set.

Mean, Median, Mode

The mean (also called the average) of a data set is one of the most used and abused statistical tools for determining central tendency. It is the most used because it is the easiest to apply. It is the most abused because of a lack of understanding of its limitations.

In a normally distributed data set, the mean (average) is the statistical tool of choice for determining central tendency. We use averages every day to make comparisons of all kinds such as batting averages, gas mileage, and school grades.

One weakness of the mean is that it tells nothing about segmentation in the data. Consider the batting average of a professional baseball player. It might be said that he bats .300 (Meaning a 30 percent success rate), but this does not mean that on a given night he will bat .300. In fact, this rarely happens. A closer evaluation reveals that he bats .200 against left-handed pitchers and .350 against right-handed pitchers. He also bats close to .400 at home and .250 on the road. What results is a family of distributions

As can be seen, the overall batting average of this baseball player does not do a good job of predicting the actual ability of this athlete on a given night. Instead, coaches use specific averages for specific situations. That way they can predict who will best support the team’s offense, given a specific pitcher and game location. This is a common situation with data sets. Many processes produce data that represent families of distributions, like those in the diagram above. Knowledge of these data characteristics can tell a lot about how a process behaves.

Another weakness of the mean is that it does not give the true central tendency of skewed distributions. An example would be a call center’s cycle time for handling calls.
If you were to diagram call center cycle time data, you would see how the mean is shifted to the right due to the skewedness of the distribution. This happens because we calculate the mean from the magnitudes of the individual observations. The data points to the right have a higher magnitude and bias the calculation, even though they have lower frequencies. What we need in this case is a method that establishes central tendency without “magnitude bias”. There are two ways of doing this: the median and the mode.

The median is the middle of the data set, when arranged in order of smallest to largest. If there are nine data points, as in the number set below, then five is the median of the set. If another three is added to the number set, the median would be 4.5 (the mid-point of the data set residing between 4 and 5).

1 2 3 4 5 6 7 8 9 1 2 3 3 4 5 6 7 8 9

The mode, on the other hand, is a measure of central tendency that represents the most frequently observed value or range of values. In the data set below, the central tendency as described by the mode, is three. Note that the median is 4.5 and the mean is 4.8, indicating that the distribution is skewed to the right.

1 2 3 3 4 5 6 7 8 9

The mode is most useful when the data set has more than one segment, is badly skewed, or it is necessary to eliminate the effect of extreme values. An example of a segmented data set would the observed height of all thirty-year-old people in a town. This data set would have two peaks, because it is made up of two segments. The male and female data points would form two separate distributions, and as a result, the combined distribution would have two modes.

In this data set, the mean would be 5.5 and the median would be of similar magnitude. Using the mean or median to predict the next person’s height would not be of value. Instead, knowing the gender of the next person would allow the use of the appropriate mode. This would result in a better predictor of the next person’s height.

In other words, the appropriate method of calculating central tendency is dependent upon the nature of the data. In a non-skewed distribution of data, the mean, median, and mode are equally suited to define central tendency. They are, in fact right on top of each other.

In a skewed distribution, like that of the call center mentioned earlier, the mean, median, and mode are all different. For prediction purposes, with a skewed distribution, the mean is of little value. The median and the mode would better predictors, but each tells a different story. Which is best depends upon why the data is skewed and how the result will be used.

A shift in the process’ output can make a data set seem skewed. In that case, the recent data is evidence of special cause variation. It means that the data set is on the way to becoming bi-modal, not skewed. For example, consider measuring the height of all thirty-year-old-people in a town as above. If females are measured first, there will be a normally distributed data set centered around 5 feet. As the men begin to be measured, the date set will begin to take on a skewed look. Eventually, the data set will become bi-modal. This phenomenon can make statistical decision making difficult. The key is to understand the reason for the data set’s skewedness.

The lesson to be learned here is that things are not always what they seem to be. You have to know what is happening behind the numbers to make the correct decision about how to calculate central tendency.

Understanding the nature of the data is also critical to making good choices about which statistical tools to use. Many poor conclusions find their origin in a lack of data intelligence.

In summary, as a rule, the mean is most useful when the data set is not skewed or multi-modal. Either the median or mode is useful when the data set is skewed, depending upon why it is skewed. The mode is most useful when the data set is multi-modal. Under all circumstances, the nature of the data will dictate which measure of central tendency will be best.

Pursue Your Dreams

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My mentor told me that I should pursue my dreams.  Find the people who are the best in class in the talents I need, and learn from them by adding value to their dreams. By making a positive exchange in value with people, everyone is a winner.  Sounds like something Zig Zigler would have said.

He also told me to avoid those who would gold brick off of my talents and success. People who would create a negative exchange of value with me. There is no upside to this scenario.  Helping people is great.  Being a doormat is not.

The first point requires hard work.  The second can happen with no effort on your part.

When swimming the deep water of hard work and sacrifice, partner with a life vest, not a concrete block.

 

Project Management

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A current project I am working on involves 4 companies. The principle, a web services company, an electronic hardware and firmware company, and a contract manufacturer. I am using a traditional Gantt tool, along with Excel, to manage the overall project. We rely on each of the other companies to have their own internal project management tools. The contract manufacturer uses a traditional Gantt tool to manage their multiple projects both corporately and individually. The hardware/firmware company also uses a traditional Gantt tool. The web services company is using their own in house project tracking strategy. None of the companies involved use Agile tools.

It is better, in my opinion, for software and firmware developers to operate with Agile. Both the web services company and the hardware/firmware companies have had their struggles and would have benefitted from an Agile approach to their project management strategies. The principles’ use of a traditional Gantt tool is adequate for project management on a macro level, but the use of Excel to “break out” tasks, and groups of tasks, on a micro level is necessary for seeing detail. The principle is managing both their own tasks and those of the contractor companies.

Throughout the project we have met weekly as a group. Some by phone and some in person, the logistics of the meetings dictating which. We have also met at least twice a week one on one with our contractors. This was done by phone early on, and face to face over the past few months. It involves some travel, which is why we chose contractors local to the principle.

The meetings are focused on three areas. Where we are now, make work ready (upcoming tasks) and what problems or obstacles may be in our path. This is meant to get everyone on the same page and to share problems and opportunities. Some issues create addition meetings between the engineers off line. All meetings are documented and emailed to the entire team. This way, only those needed at these ad hoc meetings have to attend.

Projects are like funnels. In the beginning, there are more tasks in play at the same time. There is lower velocity and lower friction between the individuals and the businesses they represent. The work is focused on bringing all tasks to an eventual assembly of the final product or service. As problems and setbacks occur you should attempt to evaluate their impact on future tasks and the completion of the project. The objectives are to deliver the desired project results, on time and in budget.

All tasks should have an operation definition that includes what it is, who is responsible, how it is to be accomplished (tools and resources), a start date, a completion date, and a definition of what complete means. This is where most projects fail. Either this operational definition is not fully laid out or it is ignored as pressure to finish mounts up.

Maybe the most important part of project management is trust. As the project moves down the funnel, both velocity and friction increase. As pressure mounts toward the end of a project, all the hedging done earlier will land in your lap. The way to prevent this is to divide the project into segments. We have an “end of the week” focus. It is part of the weekly meeting format. Things are due when they are due, unless the project manager and partners agree to slippage. Slippage is not necessarily failure, unless it is not disclosed. Seeing problems early can control the damage from unexpected negative events.

I find that a master project plan can be difficult to use effectively on a micro level. I find it better to have the project mapped out in segments based upon the master project plan. This makes it easier to use break out tools to manage the project on a daily and weekly basis. It also makes it easier to see and handle the unexpected.

Project management can be rewarding or stressful. Reducing stress requires a good plan, a commitment to stay on track and excellent communication. I have already mentioned trust, which is the foundation of everything in the previous sentence.

Reluctance to distribute bad news, or hedging, will only increase stress and the probability of not meeting project objectives. This is something that senior management can make easy or hard. Shooting the messenger will make it harder for the project to succeed. Move quickly to state both bad news and what is being done about it.

Everyone needs to have a realist perspective on time lines and budgets. In the current project, we took the shortest possible time, plus the worst case time, plus four times the most probable time. This was divided by six to come up with a good faith project estimate. This works pretty good unless someone in senior management only considers the shortest possible time line and builds that into their expectations. The earlier this type of problem is addressed the better.

Remember, it were easy, everyone would be doing it. The bigger the project and its impact, the more difficult it can be. At the same time the more rewarding it can be.

Forward Thinking

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It is not enough to just innovate around a tried and true point of reference.  To survive and thrive you must be willing create a “new” tried and true point of reference, continuously, and in real time with the market.  I can remember when my team first introduced the asTech technology to the collision repair industry.  We were traveling to conferences doing demos for so called experts.  It was common to hear, “I don’t believe them.  It’s just smoke and mirrors”.   Most of those folks are not considered experts anymore because we moved the needle on what was possible.

 You can spend your whole career and never get a chance to make a difference in the market place.  What will folks say about you in 10 years?  Be the writer of this script, not the reader.

 The article below is example of accepting the status quo.  This is not the script I want to write for myself.

Nokia CEO ended his speech saying this “we didn’t do anything wrong, but somehow, we lost”. By: Ziyad Jawabra

Nokia CEO ended his speech saying this “we didn’t do anything wrong, but somehow, we lost”.By: Ziyad Jawabra

During the press conference to announce NOKIA being acquired by Microsoft, Nokia CEO ended his speech saying this “we didn’t do anything wrong, but somehow, we lost”. Upon saying that, all his management team, himself included, teared sadly.

Nokia has been a respectable company. They didn’t do anything wrong in their business, however, the world changed too fast. Their opponents were too powerful.

They missed out on learning, they missed out on changing, and thus they lost the opportunity at hand to make it big. Not only did they miss the opportunity to earn big money, they lost their chance of survival.

The message of this story is, if you don’t change, you shall be removed from the competition.

It’s not wrong if you don’t want to learn new things. However, if your thoughts and mindset cannot catch up with time, you will be eliminated.

Conclusion:
1. The advantage you have yesterday, will be replaced by the trends of tomorrow. You don’t have to do anything wrong, as long as your competitors catch the wave and do it RIGHT, you can lose out and fail.

1.     To change and improve yourself is giving yourself a second chance. To be forced by others to change, is like being discarded.

Those who refuse to learn & improve, will definitely one day become redundant & not relevant to the industry. They will learn the lesson in a hard & expensive way.

Building Great Teams

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I did some research on team building recently.  What I found were lists of qualities that define effective teams.  The problem is that these lists are typically filled with descriptions of characteristics that are superficial.  I can say, or do, whatever is necessary, when it is necessary, so that I look like a great teammate on a great team.

I believe that building a great team requires great teammates. It is much more personal than a list of qualities. You do not want to build a house on a foundation of sand and you do not want to build a team on a foundation of individuals whose sole focus is on their own personal value propositions.

Dwight L. Moody said that “Character is what you are in the dark”, meaning that you express your true character when your potential duplicity is difficult to discover. You express your character in what you do, not what you say.

I like to associate teammates to shipmates.  This association strengthens the concept of teamwork.  When at sea, if the ship sinks, everyone gets wet.  In the most powerful definition of teamwork, everyone succeeds together or fails together. There are no special cases, unless someone places their own goals above that of the team.  This would be called sub-optimization.

You cannot build a great team from individuals who make excuses, criticize, are too busy to help others, or are unwilling to step out of their comfort zone.  In Warren Bennis’s book “Organizing Genius”, he describes the characteristic of great teams like the Skunk Works, Disney Studios, Apple, and the Manhattan Project.  These teams were built on personal sacrifice, cross functional activities (folks worked on what needed worked on no matter whose job it was), a commitment to each other and the project, a lack of respect for outside authority, an intolerance for individuals who did not fit the culture, and a supreme belief that they comprised the best of the best as a team.

What kind of shipmate are you?  The quote below is from a man who served in every branch of the military.  He was known for his ability to build successful teams in difficult circumstances.

“You gotta stop and think about your shipmates. That’s what makes you a great person and a great leader – taking care of each other. You’ve got to think — team. It takes a team to win any battle, not an individual.”  Courtland R. “Corky” Johnson

Building New Skills

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Much of our frustration with personal development comes from our failure to establish short term goals.  This frustration springs from a failure to understand that the learning and development of skills is typically an evolutionary process.  Your brain learns by building neural connections over time, by way of practice and integration into your current understandings and skills.

Maybe you want to learn to play a musical instrument. The first day you pick up the instrument, you will not play it like a virtuoso.  You correct for this by expecting a certain level of accomplishment for each practice.  Meeting this goal gives you a positive view of your efforts.  You repeat this cycle over and over again, like climbing a ladder.

The excuse, “It’s too hard”, is usually based upon unrealistic daily or weekly goals. It is exceptionally difficult to eat the elephant in one bite.  You have to break it down into manageable pieces.

Another example might be reading a text book.  Your goal for the week may be, “I need to know Chapter 5 for a test this Friday”, but what is today’s goal, tomorrow’s goal, and so on?  If you want to feel good about your progress, divide and conquer the material.

  • I need to understand section 5.1, Monday.
  • I need to understand sections 5.1 and 5.2, Tuesday.
  • I need to understand sections 5.1, 5.2 and 5.3, Wednesday.
  • I need to understand sections 5.1, 5.2, 5.3 and 5.4, Thursday.
  • I need to be ready to take the test Friday at 2 PM.

This process allows you to feel a sense of accomplishment every day. Your focus is on what you need to accomplish right now, instead of what is needed for the entire week.  A smaller bite yields a less stressful and more fulfilling experience.  It also allows the pieces of the material you are learning right now to “sink in” before you learn the next piece (text books are written around this type of learning model).

Here is how you do it. If I am asking for 3 ½ hours of your time per week to work on something, that is only 30 minutes a day.  Thirty minutes a day is easier to manage than 3 ½ hours at one time, and it is more effective.

If you are learning golf, taking a long trip, learning a new skill, etc., break the whole into pieces. Then you can knock them out one at a time until you reach your goal.  This involves living in the moment.

  • In golf, you can’t hit the ball like a pro, who is hitting at least 100 practice balls a day, by hitting 50 competition balls a week.
  • You can only drive the stretch of road you are on, no matter how much you want to think about the last mile of your trip.
  • You break old habits, and form new habits, by repetitive actions and thoughts.
  • You learn new skills by practice.

You can institutionalize imperfection by practicing something imperfectly, thereby making a bad habit.  You can institutionalize perfection by practicing something perfectly, thereby making a good habit.  Have you ever seen someone with perfect form, great patience, or great instincts?  They got there by way of perfect practice. The training of their mind and body to accomplish the goal right in front of them.

Innovation and Creativity in Motion

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Many of the activities and strategies we use to innovate and manage are actually road blocks to creativity and innovation. Certainly, the enforcement of a time line and being cost conscience, are important, but only in respect to their appropriate place in the life cycle of a product or service.  When applied to the creative and innovative phases in this life cycle, they are disruptive and cause sub-optimization.

Innovation is a creative process that requires open-mindedness and a safe environment.  Creativity and innovation are processes that rely upon failure and the ability to learn from failure. You cannot create or innovate where failure is unacceptable or penalized.

Formatted business meetings and project management meetings are not events for innovation. They are events for business management. Important?  Yes, but not in the innovative process.  In these venues, failure is a negative thing and, “when will the project be completed?”, is the primary question. In the innovative stages of a project “what to do?” or “how to do it?” are the main questions.  Other thoughts get in the way.

What I am about to say will make control oriented managers uncomfortable.  You cannot control creativity, you can only feed it or starve it.  When a work group or team is in the creative or innovative mode, just get out-of-the-way. Command and control must give way to facilitation. You are better off guarding the door to keep creativity starving people and systems out until it is time for them.

When a work group or team is working in the creative and innovative phases of a project, questions like who gets the credit, cost, who is smarter, and how fast can we get done,  take a back seat to collaboration. It is an inclusive environment instead of an exclusive one.

Here are some ideas to support creativity and innovation. First, casual dialogue centered loosely around a topic opens up the possibility of seeing things from multiple perspectives, thus eliminating an error in parallax. This is the way great minds like Einstein’s worked. It is also how high-performance work teams think.

It’s not about discussing a specific aspect of the project so much as it is a general meandering dialogue. There is more storytelling and analogies than would take place in a typical development or project meeting.  Meetings away from one’s work desk or controls are great for this type of thinking.

It is a safe environment where people are allowed to get out of the box. People who are not the exerts on a particular topic get to offer their perspective, forcing the experts on that topic to think through a response to their questions and suggestions. It is a movement away from what we think we believe, to true understanding. The result is innovation and creativity in motion.

Second, there need to be creativity/innovation zones in the work areas.  These are spaces where folks can talk, argue and “sharpen the sword” with each other.  Employees do not go there to work, they go there to think creatively.  This space is divided into group “think tank” areas and individual “thinking out of the box” areas.  They are not anyone’s personal space, they are not scheduled spaces, and they are only for the creative/innovative processes and folks.

Lastly, encourage dialog between workgroup/team members that have little format, other that a place and time.  As a line manager, you may want to stay out of these meetings and be informed by way standing project meetings later. This is definitely a “watched pot never boils” situation.  Manage creativity and innovation by staying out of the middle of it.  This means facilitation instead of control.

High Performance Work Group Manifesto

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High Performance Work Group Manifesto:

  • Reject the “Box”.  We do not want to be categorized into anything normal or stationary.
  • Do not seek what is easy or comfortable.
  • We value problems, roadblocks and change.  We expect and seek out problems, roadblocks and change.
  • We value the team.
  • We value diversity of opinion.
  • We value the “and” and reject the “or”.  We want it the way we want it.
  • We enjoy being told that something can’t be done.  Then going out and proving the “teller” wrong.
  • We are pirates. Not conformists.
  • We are arrogant and difficult for conformists to get along with.
  • We believe we can do it.
  • We reject traditional thinking and embrace creating our own future.
  • We are not afraid to fail.  We are afraid of people who are afraid to fail.  They are the bad apples that can spoil the whole barrel.
  • We do not focus on addressing wrong answers.  This is the purview of the small minded.  Instead, we focus on addressing the wrong questions. This is the venue of really smart folks.