What do all the lines and boxes mean on a boxplot?

The Boxplot is one of simplest graphical tools to look at, and a tool I use very frequently when first reviewing my data sets. It is a great visual tool for showing the variation and average of a data set, that is not sensitive to outliers (nonparametric approach). The chart shows how the data breaks down by categories, to help you identify areas of concern or potential causes of your problem.

However, it is the most confusing chart to explain how each piece of the box is calculated. When teaching a basic statistics class, I actually avoid discussing the boxplot, because it brings about many questions and becomes a distraction for the class attendees.

When we look at the boxplot simplistically, it gives us a quick understanding of our data. Let's look at an example from Minitab.

You should be able to draw some simple conclusions from the chart

• The boxplot for the paint data shows that paint blend 4 has both the highest median and least variability, with an interquartile range of only 3.10.
• Blends 1 and 3 appear to have roughly similar medians and variability.
• Blend 2 has the lowest median and greatest variability, with an interquartile range of 11.72. The short whiskers indicate clumps of data near the box endpoints.
• There are no outliers in the data

Ultimately, the very next question is always "how are the box and lines calculated?"

Let's breakdown the chart to help clarify it.

1. Determine Median (50th percentile) = 146
2. Determine 1st quartile (25th percentile) = 141.5
3. Determine 3rd quartile (75th percentile) = 150
4. Calculate outlier range “whiskers” as (1.5 * (Q3-Q1)) = 12.75 from median (133.25 to 158.75)
5. Calculate Interquartile Range (IQR) by taking Q3 – Q1 = 150 – 141.5 = 8.5
6. Draw line through median
7. Add asterisks if data outside outlier range

You can also download the Boxplot guide below for future reference.

Hopefully this helps you understand box plots, and you see the need to use them prior to analyzing
any data set.

8 ways why batching is bad for your business

One of the most common questions we get when reviewing a process:

"What's wrong with batching? I can produce so many more widgets when I do it this way?"

When I first started out in Lean, I had the same questions. It seems more efficient to the worker, and therefore it doesn't make sense to them that someone would want to change that. It took a few improvements before things started to sink in for me.

Just so everyone is on the same page, when you batch, you don't complete tasks one item at a time, you wait until you have a few items, then complete the task all at once. Usually this is because the time to get setup to complete the task takes a while, so it's more efficient to do the task all at once. However, the time waiting for a large enough batch to complete causes the next step to wait, then it generates a large amount of inventory all at once, which is unable to deal with the inventory and therefore it will need to be stored or will sit waiting to be worked on.

Don't believe us? Check out this video of envelope stuffing, and you'll understand why one at a time is better.


Here are a list of reasons why batching and inventory is bad:

1) Delays in detecting problems - The parts are not allowed to move to the next process until the whole batch is complete, so any problems found later in the process are delayed, adding to the number of items with problems that will need to be reworked or thrown away, increasing costs.
2) Taking up resources - Any items being produced that are not needed right now are taking up time at that process step, that could be better spent on things that are needed, which delays deliveries to customers.
3) Inventory cost - The labor and cost to process the items has been spent, but since it's not needed yet, it will take longer to get paid by the customer, which reduces cash flow and the cost of capital (money that could be getting a return on investment).
4) Cost to store inventory - Inventory needs to be stored, so there is a cost to process and record it, package it to protect it from damage, put it somewhere out of the way (requiring more floor space, which adds to the cost of utilities for lighting, heating and cooling).
5) Potential for problems - Once the inventory is stored, there is an increased chance that it gets damaged, deteriorates, corrodes, etc. This requires it to be redone or reworked or discarded, which costs money.
6) Loss of customers - If a customer cancels the order, or asks for a different version, or the part is no longer made available for sale, then the inventory becomes worthless, so the expense of buying and purchasing the items is lost.
7) Cost to dispose - There may be additional costs to deal with the scrap or unneeded items beyond the wasted labor and material costs, such as landfill disposal costs, cost to transport or pickup the items, fill out paperwork, or even properly recycle it.
8) Perception differs from reality - As seen in the video, the perception of batching may not actually result in faster processing.

Don't get me wrong, there are situations where batching is a better option in the short term (large setup times, low cost of inventory, inconsistent deliveries, etc). There are other situations, especially when ordering from a supplier, where travel and bulk discounts come into play. For these situations, an economic order quantity can be calculated that considers all these extra costs, to decide how large the batch size could be. However, in general the goal is to minimize the size of batches as much as possible by making the setup times less.

What examples do you have that helped you understand inventory and one piece flow? What other problems does inventory and batching create?