As we mentioned in the previous activity, if bins of a histogram are too wide, they may actually hide critical information that will help you understand what’s going on with the data. On the other hand, if bins are too narrow, the histogram becomes too cumbersome and variation may reflect random behavior and not significant changes.

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Monday Histogram

Hour Intervals in Work Day

Our mission in this activity is to explore how a poorly developed histogram can actually hide valuable information or at best make it difficult to decipher.

We’ll do this by walking through a scenario with a poorly-constructed histogram and a well-constructed histogram to illustrate how this might happen.

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Monday Histogram

Hour Intervals in Work Day

As Chief Financial Officer, your job analyze revenues to make sure projections and goals have been met and make new goals for the upcoming year. The 2012 fiscal year just ended. The revenue goal for your company was $200 million, but the actual revenue only ended up being $170 million. The CEO requested that you develop a revenue chart that will illustrate any patterns, so you create the histogram below.

Remember, the bin width of a histogram depends largely on what you’re trying to analyze. In your case, the CEO asked you to look for patterns that explain the missed goal.

With a quick look, you determine that with the lower revenue in Q1, Q2, and Q3, the company was unable to make the goal of $200 million. However, after taking this course, you realize that a histogram with only four bins might not be telling the full story.

You decide to create a new histogram, this time one with twelve bins—which means a 30 day interval between each bin. This will demonstrate revenue by months rather than by quarter. The histogram you generate is pictured below. The story is now much more complex and allows you to look for patterns much easier than the four bin histogram.

After exploring the histogram, you might have noticed that the months of March and April fell short on revenue, as well as the months of June, July, and August. What might have caused this suspicious drops in revenue during these months?

The company holds its annual user’s conference the last week of March and the first week of April. After analysis of this possible cause, you determine that many customers spent money on travel costs to the conference instead of buying your product. Also, salespersons were heavily involved in the marketing ramp up before the conference and in scheduling spots for 2013 after, which means they had less time to sell in March and April.

As for the months of June, July, and August, you checked PTO records and found that many sales employees took vacations in the summer months. In addition, many tradeshows are held during summer months which involve salespersons as exhibitors. The tradeshows are valuable marketing venues, but it also means that while exhibiting at the tradeshows, the salespeople are not on the phones selling product.

The first histogram showing revenue by quarter identified three quarters falling short of targets; however, just looking at that the four bins makes it very difficult to pinpoint the cause of the problem.

The second histogram showing revenue by month was much more helpful because it keyed you in to dramatically low revenue months, facts hidden in the first histogram.

LETS RECAP!

If bins in a histogram are too wide or too narrow, important information may be overlooked or misrepresented due to random variations. It’s important to have accurate bin numbers and widths to ensure that a histogram is not hiding an important part of the story.

CRITICAL THINKING: What can you do to tell the difference between a random variation and a data pattern that could indicate a problem?

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