Lying With Statistics – Stay Off The Median?

There are two types of numbers.  There are numbers that are near the middle and there are numbers that are on the ends.  Being a person with a last name that starts with the letter ‘L’, I can identify with the numbers in the middle.  Whenever we lined up in alphabetical order in school, that is where I was.  Today, we are going to learn the value of that.

Median is another fancy name for average.  Usually you hear it on the new when people are talking about median income, median house price, or median household net worth.  And that is because, as we will see shortly, that gives a different result than the mean, which we discussed yesterday.

The Median is just the middle number in any group.  In the group 3,4,5,11,12, the Median is 5.  There are two values below it and two above.  The Mean, incidentally, is 7.  The Median is handy to use in groups of numbers that have extreme outliers, like incomes, home prices, or net worth.  For example, let’s say in your neighborhood, people have a median income of $51,500, their homes are worth a median price of $189,000, and the Median household net worth is $70,000.  These numbers are important because, among other uses, they are used to calculate taxes.

Then a billionaire builds a multi-million dollar house in your neighborhood.   How much does the Median price move?  Very little, if at all.  All that happened is that there is one more number at the top of the list.

But how would this affect the Mean?  Let’s look at some concrete examples.  For the state of Maine, in 2011, the top 1% of income tax filers had an income of over $800,000.   As you can see on this site, that makes the Mean income, $61,081, substantially higher than the Median, $47,849.  If your whole town is valued that way, that is going to make a big difference in tax calculations.  That is going to be the same with home prices and net worth.  Do you think all of those big, fancy houses on the coast are going to make the Mean higher or lower?  (Hint: higher)

Let’s Check In With Yesterday’s Examples

Let’s look at our examples and see where the Median makes sense and where we can use it to get some false conclusions:

  1. A ‘C’ in class is average.  The median grade still does not help a lot.  Ruling: TBA
  2. The average balance for the deposits at your bank is $5000.  Using the population of  10 customers with a balance of $40,000 and 90 customers with a balance of about $1100, the Median is going to be $1100.  Because that is how much the 50th customer in order of balance has.  If the balances follow a power-law distribution, the Median will still be below the Mean.  If you are running this branch, this is not going to look good.  Ruling: Bogus
  3. The average height of a woman in the US is about 5’4″.  Remember from yesterday that this group fits a normal distribution (or bell-curve) very nicely.  The Median will give you about the same result as the Mean.  Ruling: Winner!  But use the Mean because it is easier to explain.
  4. The average patient stay at a given hospital is 2.5 days. This one is similar to the average deposit balance.  The vast majority of your patients can be staying 2 days or less, but one 90 patient day does not wrecks all of your numbers.  Ruling: Winner! But you still have to note the outliers to be honest.

The Median is very useful in populations that do not follow a Bell Curve.  But don’t go crazy with it.  It is another tool that can be used for good or evil.  In many cases, a little more evil than the Mean because the Median is not as well understood.

The image on this post is from


Lying With Statistics – Using The Average: Don’t Be Mean

Average seems like such a simple word.  A ‘C’ in a class is average.  The average height of a woman is about 5’4″.  The average balance for the deposits at your bank can be $5000.  The average patient stay at a given hospital is 2.5 days.

These all seem reasonable.  But are they?

When you think of average, you probably think back to middle school math and remember that to get the average of a group of figures, you just add them all up and divide that total by the number of figures.  So the average of 4,6,8,2,5 = 25 divided by 5 (the number of figures).  The answer is 5.  In the statistical world, this is called the Mean.  When most people hear the word ‘average’, they automatically think of this.

This is very simple.  And the value is going to be a good way to generalize about a group of numbers.  Or to lie about it…

Let’s Get Mean About The Mean

Let’s look at our examples and see where the Mean makes sense and where we can use it to get some false conclusions:

  1. A ‘C’ in class is average.  This is actually folklore, unless a professor is grading on a very rigid curve, which most do not.  Someone averaging a C in college is barely going to graduate.  There are definitely more people graduating with A’s than F’s.  And at some colleges, like Harvard, the average grade is much higher.   ‘C’ just means average in our lexicon.  Ruling: TBA
  2. The average balance for the deposits at your bank is $5000.  This number is a little too round to be true and that is because I made it up.  But, think about this.  You can have 100 customers all with a balance of $5000.  Easy math.  Or you can have 10 customer with a balance of $40,000 and 90 customers with a balance of about $1100.  More likely, the balance will follow a power-law distribution, where the top 10 percent of depositors have well over half the money.  So, who is your average customer?  You really don’t have one.  Ruling: Bogus
  3. The average height of a woman in the US is about 5’4″.  Think of all of the women that you know?  How many are 2 feet tall?  How many are 28 feet tall?  I am going to guess that the number is 0.  In fact, most of the women that you know are probably between 5′ and 5’8″.  And this group fits a normal distribution (or bell-curve) very nicely.  So average is easy to visualize and will not vary much for any random group of women.  Ruling: Winner!
  4. The average patient stay at a given hospital is 2.5 days. This one is similar to the average deposit balance.  The vast majority of your patients can be staying 2 days or less, but one 90 patient day stay wrecks all of your numbers.  Ruling: Bogus

You can apply a Mean to any group of numbers.  That does not always indicate that it is appropriate to use.  And it is easy to use to mislead, which is wrong.  So don’t do that.

Next we will cover the Median and the Mode, other ways that can be used (and abused) to show an average.

Value – What It Is, Why It Is Different For Everyone

Providing value.  That sounds like something that you hear at a thrift store.  Or somewhere that sells used car parts.  The fact is that you should hear it anywhere you work, for any service you provide, and for any product you produce.  The customer should feel like they got a little more than the paid for, no matter if you are selling a used book or a luxury car.

At, value is defined as, “relative worth, merit, or importance.”  That determination can only be made by the customer.  There is no reference to price.  Things from socks to yachts get sold every day and people buy what they feel to be the best deal.  But what makes that best deal?  It could be:

  • The lowest-cost item they can find
  • The best customer service
  • The best support for the product after the purchase
  • The flashest, biggest, most impressive product
  • Something else or some combination of the above.

Stores provide service in many different ways.  They position themselves in one or more of those niches.  For instance, if you are a bank, you want to be able to draw customers with the best rates.  But there are a million banks out there and someone will always have a better rate.  You can provide a competitive rate and brilliant customer service and support.  That is the little bit extra that the customer feels they are getting for free, enough to outweigh some tiny bit of interest.  There is there the value is.

At a hospital, you provide the same services, to a large extent, as any other hospital your size.  How well do you do it all?  How do you treat your patients?  How do you follow up to determine outcomes and constantly work to improve them for every patient?  Answering those questions leads to value for the patient.  After all, the patient is a customer, too.

As an employee, no matter what your role, you need to provide value to both your employer and your customer.  That means using your talents to be the best at what you do.  It does not mean being better than everyone else at everything.  But you are better at something.  Find a way to use whatever your talents are to make a difference.  That can start with something as simple as a genuine smile.

We live in a world of instantaneous information sharing.  More than ever before, your reputation is what makes or breaks you.  Pick your value providing strategy and go.  Establish a reputation of excellence and you have also established a reputation of providing value.  Just remember, in the end, it is the customer that really determines that.

Average – Is That What You Want?

Statistics.  Did you just shudder when I said that word?  People are very dipolar about taking statistics classes.  Either they loved it or hated it.  Most are in the second group.  I think it is because they are so darn counterintuitive.  Which is why it is easy to use them to back up any point you want to make.

A friend of mine gave me a great book, named How To Lie With Statistics by Darrell Huff.  It was published in the 1954, so the numbers are a little dated, but the lessons are great.  It is a quick read and allows you to pick up on numbers that don’t quite look right.

Take the average, for instance.  I can tell you that the average high temperature in April in Portland, Maine is 53 degrees.  That says nothing about the daily fluctuations.  The record high was 89 degrees.  The record low was 8 degrees.  That is a lot of variability to be ready for, 81 degrees.  San Diego, California, on the other hand, has an average high of 61 in April, with record high and low of 98 and 41, respectively, only 57 degrees apart.  If you want a guarantee of a frost free April, go to San Diego.  But the average does not tell you that.

Another way to render an average meaningless is to conveniently not specify the data you used to calculate it.  Today, on, the median cost of a house in Portland, Maine is listed as $236,000.  At, the median cost is listed as $379,450.  That is a big difference!  It might meant the difference between you thinking it was reasonable to move there or not.  The difference probably comes from the area each is calling “Portland, Maine”.

So, when you look at an average, make sure you dig a little deeper.

Next post, I will talk about the different types of averages and how to interpret them.

Feedback – A River Of Ideas

Every process that you have put in place has been a finished process.  No changes needed.  Which number below best matches your answer?

  1. Right.
  2. Right?
  3. There may have been a few exceptions.
  4. All of them change over time.

If your answer was number one, you can stop reading.  Number two, you have some research to do.  Number three, you might also want do to a little checking.  If you selected number four, you live in the real world.  Keep on reading.

There are a few different ways to get feedback.

  • You can talk to people involved in different steps in a process, singly or in groups.  This is a very good idea.
  • You can walk through steps in a process or a whole process with one or more people.  This is called Gemba.  Also a great idea.
  • You can provide an easy way for people to submit ideas for improvements and new processes.  Again, very positive.
  • You can create a culture that encourages feedback and new ideas.  One that rewards people for making positive changes for the customer, other staff members, and the company.  In my opinion, this is the best idea.

The first three items are things that you can do right now, anywhere, at any time.  You don’t even have to be tracking down a problem.  In fact, if you just show up out of the blue and start asking how you can make people’s lives better, you will immediately start down the road of the fourth point.  If you follow through.  All of the first three items will help you with the fourth.

In my experience, people are looking to contribute and help.  They are looking for a conduit that allows them to do so.  Think of it like a river.  A river starts as one or more  streams.  And it gets larger as it goes along and more streams join it.  It works the same way with positive change.  You have to work at making sure there is nothing damming or blocking those streams or the river.  Because those are ideas flowing down that river.  Sure, some of them might not be great or feasible right now, but some of them will be pure gold.

Get them out into the flow where you can use them.

Communication – What To Share

Yesterday, I talked about how to streamline communication using email so it would be quick to read and understand.  Today I am going to write about what to communicate.  I can’t know what business you are in or service you provide, but I think there are some good general standards that can be followed.

I am going to reference Work Rules! by Laszlo Bock again.  Google has weekly all hands meetings with the president of the company that people can attend in person or virtually and where anyone can ask any question.  And even better, they can expect an answer.  This is a great way too have accountability on both the executive and staff side.  If staff are going to be encouraged to ask hard questions, they’re going to expect honest answers.  If the executives are hearing good, thoughtful questions, they know what that the staff is engaged, taking the forum seriously, and feeling that they are getting honest answers.

Communication goes beyond that though.  At any company the owner or the upper management decide what type of information to pass along to the staff.  In the past, this was easier because companies had a more hierarchical approach to their organization.  But in the present day, while the reporting hierarchy is still there, people are being hired for their ideas and ability to innovate as much as they being hired to do a specific job.  In order to do that, they need as much information as possible about the company’s long-term and short-term goals.  The need to know about the company’s major initiatives, whether they be new products, quality initiatives, sales efforts, and how the company is performing.  Not only does that help employees make better decisions, it allows them to contribute their insights into helping the company thrive.  It also keeps them focused on work that is in keeping with company goals.

So when considering all of this in considering what information to disseminate, keep in mind another idea from Google that I touched on in a previous post.  Managers there are encouraged to give more freedom to the staff than they generally feel comfortable with.  Getting more information to your staff then you would traditionally feel comfortable with is going to

  • serve the purpose of enabling them and make it possible for them to do things that match the company’s direction in a more focused and efficient way.
  • establish trust.  If they know you are sharing good and bad information, that will help them share as well.
  • create a very team-like environment where people are willing to go beyond their roles and do what is important for the company.

Obviously, with all of this said, you cannot share everything.  But you can probably share more than you do.  When you do that, look for great things to happen!

Communication – Don’t Use A Fire Hose

There is a term called drinking from the fire hose.  If you have ever felt like you were trying to do that in order to keep up with just your emails, let alone phone calls, news, and even blog posts, welcome to this blog post.

We live in a society today where disseminating your thoughts, ideas, reports, and anything else is extremely easy.  And it is extremely easy to open yourself up for those communications.  The problem is that then there is too much for any one person to process.  Just like drinking from a fire hose, you cannot take it all in and you are going to be a mess in the process.

Just using the work example; emails, texts, and phone calls are probably the three major communication tools that are used.  Let’s talk about emails.  Most people get far too many.  The import emails, the ones you really need to read and understand, are buried in your inbox with the non-pertinent emails.  And even the important emails are often not written concisely.  On top of that, most people’s jobs are not centered around reading e-mail.  For emails to be really effective two things have to happen.  That has the first is that emails need to be clear, concise, and to the point.  The second thing is that, as an organization, there needs to be education about appropriate use of e-mail.

In order to write a good e-mail that is going to be read and understood there are only a few rules that you need to follow.

  1. The subject describes what the e-mail is about.  Using forwards and replies without changing topics is a good way to have an e-mail go unread.
  2. Make sure that the list of people you send e-mail to it is appropriate.  Don’t include people who are not going to be interested and make sure you include all of the relevent people.
  3. The first two or three sentences in the body of the e-mail should contain a summary along with any conclusions.  If you are describing a meeting, any major decisions and news is good information to put at the beginning.  You can devote other paragraphs further down to details.

The second key about emails is that, as an organization, you need to educate your people about using email appropriately.

  1. Like any other kind of communication, it is OK for people to specify what they want and how they would like to receive it.  This leads to a conversation and ultimately to the compromise or a change in process so that both the sender and receiver of information are satisfied.
  2. It is important to educate people to consciously decide what emails if they want to receive.  Some are mandatory.  But beyond that, most people have options to receive emails from vendors, notifications about projects, are copied on emails from former work assignments, and many other sources.  It is important for them to recognize that they probably cannot read all of these and to pare their list down so that they are only getting emails that are important to them.
  3. There needs to be a conscious effort on the part of management to set a good example.  People learning the protocols will naturally look to you.
  4. Schedule important communications at a regular time and day.  Once people begin to expect important news on a schedule, they will be much more likely to look for it.

I concentrated on emails today because that seems to be the most common mass communication tool used in businesses.  People that distribute a lot of emails are under the assumption that the emails are being read and actions are being taken in accordance with the directions given.  That needs to be more than an assumption.

You have to take the time as an organization or a team to make sure those communications are being read and understood.


Communication – Let’s Talk About It

Robbie: [Linda shows up for the first time after failing to marry him] You’re late.

Linda: [sighs] I’m sorry… I just couldn’t do it.

Robbie: Well, if you need more time, I guess I could wait.

Linda: No… I don’t need more time, Robbie. I don’t ever want to marry you.

Robbie: [takes a deep breath, sighs] Gee, you know that information… really would’ve been more useful to me *yesterday.*  (from The Wedding Singer)

How often has something like that happened to you?

Most of the time, unshared information is not quite that dramatic, but it can have an outsized impact on teams working together.  If there is not good information sharing, members of a team can lose trust in each other very quickly, even if the cause is completely innocuous.  Staff can lose confidence in management and vice versa.  Customers can lose confidence in your services.  Lots of bad things can happen.

The good news is that this is easy to address.  Just like a successful business, there are three things you need to do:

  1. Communicate
  2. Communicate
  3. Communicate

And remember that this goes both ways.  There is the person sharing and the person receiving.  Both have to participate in this process, so it is incumbent on internal parties to make sure that the chosen method works well.  With customers, you have to ask a lot of questions and collect hard data to make sure your messages are reaching the right people in a timely manner.

There are approximately a million different ways to communicate now.  In person, phone, email, blogs, text messaging, instant messaging, an unfathomable number of social network platforms.  They key is finding the one that works and also finding the pattern that works.  This may take some trials to figure out the best method.  Emailing someone late on Friday afternoons is not the best strategy for success.  Establishing a weekly schedule of reporting would be much better.  Setting the expectation up front always helps.

Another thing to remember is that people receive information differently.   You might need to send your message using multiple methods, depending on the variety of your audience.  You need to solicit feedback to find out if they are working.  Just assuming that your message is being delivered, especially if it has to go through multiple layers of staff, is not a good plan.

On the other end, to be a good receiver of information, you have to try to be a little flexible.  You will get messages by various means and need to pay attention.  You also need to provide feedback on what methods work the best.  If there is two-way sharing going on, then people will adapt on both ends and the communication process will improve.

The last thing to remember is that communication is a process and you can look for all of the wastes that were covered in the last ten posts.  And just like any other process, addressing them will go a long way to making sure you have the best communication out there.


How Do Your Customers Benefit From Fixing Waste?

Over the last 9 posts, including the summary, we looked at the types of waste to look for in processes.  We also touched on the fact that one type of waste can lead to one or more additional types, such as waiting leading to inventory buildup and staff underutilization.  The great thing about that is that if you address the root cause for one of those, you will address the root cause for all of them.

And in my experience, that is often how this works.  Fixing a transportation issue suddenly means that you are finishing work in half of the time.  Even if a lot of that was just waiting between steps, that means that you have less unfinished inventory, physical or virtual, in process.

What does this mean to the customer?  After all, nothing we have talked about is directly related to how we work with or what we provide to the customer?  Or is it?

I would argue that it is and that your customer service will improve, sometimes dramatically, if you can eliminate waste from your processes.  After all, all of your processes lead in some manner to a product or service for your customer.  Going through the 8 types, here is how your customer will benefit.

  • Transportation – Addressing this will lead to time savings and getting the product or service to the customer faster while decreasing the risk of defects.
  • Inventory – Anything sitting around has the chance to become lost, stolen, damaged, corrupted.  Plus it can get in the way.  It is embarrasing to tell a customer you lost something.  And decreasing inventory means you are providing faster service.
  • Motion – This is another area where you can save time and reduce defects as well as have a positive effect on your staff
  • Waiting – The less of this, the faster the product or service is delivered to the customer.
  • Overproduction – Eliminating this means that you have the products and services that the customer wants when they want them.
  • Overprocessing – Means a faster delivery to the customer and helps eliminate products or services that the customer does not want, making your delivery of the desired products or services that much more efficient.
  • Defects – No customer likes a product with a problem.  Or a delay due to a bad part.
  • Staff – The front end staff will provide amazing guidance on how to serve the customer better.  That will flow through all levels.

So, when looking for waste in processes, don’t be concerned about what type it is.  Fixing one type will often fix another.  It will help your bottom line and it will help your customer service.  That combination does not happen every day.  So get to it!

Staff – Your Greatest Resource

Today is the final Tim Woods day, S for Staff.  Underutilized staff talent can be the greatest waste possible.  Recognizing and engaging the talents of your staff will lead to the greatest innovations.

There are three primary ways in which staff is underutilized:

  • They are hired to a certain set of tasks, but spend their time on other tasks.
  • They are not encouraged to speak up or innovate.
  • They are not involved in problem solving.

As a manager or a project manager, part of your role to clear the way for people to contribute.  This could mean

  • training, both in process improvement methods and also in how to communicate their ideas in a positive manner.
  • working with managers so that they know what to expect and can encourage their staff to participate.
  • spending time coaching quieter employees to help give them the confidence to express themselves.
  • spending time matching people’s skills to their roles.  Just shifting people a little to where they are best can mean huge gains for little effort.
  • actively involving multiple levels of staff in projects, so that they have ownership and become more engaged.
  • encouraging people to try new things on a small scale, even if they fail.  Encourage them to try again.  Your biggest successes will come from this.

Google is perennially listed as one of the best US companies to work for.  Laszlo Bock, SVP of People Operations at Google, in Work Rules!, describes the work dynamic between managers and staff.  The managers role is more to clear obstacles and make sure the staff have whatever they need to excel at their jobs.  This sets a high standard of work on both managers and staff.  Managers are put in a position to give staff more freedom then the manager feels comfortable with and staff have very high expectations set upon them.  Google does this across the organization by design.  And it works.

Let’s look at some math.  If you have a staff of 10 people and they are an average of only 30 years old, they have maybe 10 years of professional work experience each.  That is 100 years of work experience.  There are not many companies that have been around that long.  Those 100 years are going to have sparked some ideas and you just need to bring them out.  Even better if those 100 were not all in your business or industry.  Now you are effectively bringing in fresh talent!  All from your existing staff!

To sum up, engage your staff.  Give them the freedom and the expectation to innovate.  There is a huge, deep pool of knowledge there that just need to be let through the dam.  And you can ride that flow all of the way to success!