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Early, Late or Right on Time?
by Valerie Funk, editorial assistant

histogram is a bar graph that takes measurement data and displays their distribution to reveal the amount of variation in the data set.1 It is used to quickly analyze whether a process can meet a customer’s requirements, see whether change has occurred from one time period to another, determine whether the output of a process is normally distributed and communicate the distribution quickly and easily to others.2

To create a histogram, you must gather all data needed and separate them into data sets, which are then separated into ranges. The end result is a bar graph of the data.3

Example

Though I believe I always arrive on time for work and am in the office ready to start my day at 8 a.m. sharp, I wanted to determine the variation in my arrival times and see whether I was usually early, late or right on time. I tracked my arrival times over the course of three months (60 workdays) and plotted them in a histogram.

To prepare my graph, I listed all 60 arrival times on a piece of paper. I tallied up the different times ranging from 7:45 a.m. to 8:15 a.m. because that was the earliest and latest I had clocked in.

After the data were collected, I created a Y (vertical) and X (horizontal) axis. The Y-axis represented the number of times I arrived within a specific time range, such as between 7:45 a.m. and 7:50 a.m., over the course of 60 days. The X-axis represented the range of times I clocked in and varies over the course of 30 minutes. I then created a bar graph to represent the number of days I clocked in at each time (see Figure 1).

I arrived between 7:45 a.m. and 7:50 a.m. 18 times over the 60 days, and unfortunately, I was late and arrived between 8 a.m. and 8:15 a.m. 18 times. So what does this histogram tell me?

Types of Histograms

There are three main types of histograms (see Figure 2):

1. Bell shaped or normal: shows the normal, natural distribution of data from a process. Points are as likely to occur on one side of the average as the other. Deviations from a bell shape should be investigated, but they are not necessarily bad.

2. Skewed: shows data that are either positively skewed toward increasing values or negatively skewed toward decreasing values.

3. Double peaked or bimodal: shows two bell shaped distributions and suggests two distinct processes are at work.4

My histogram has a skewed distribution. Even though being early or on time for work is a good thing, my histogram is negatively skewed because most of my clock-in times occurred before 8 a.m., which is my actual start time.

Besides charting the time you arrive at work every morning, you can use a histogram to track production times, measure the number of defects and amount of scrap work generated by a process or track employee performance scores. Regardless of how you use it, a histogram can give you a quantitative picture of a data set over a period of time.

REFERENCES

1. ASQ and the Holmes Corp., ASQ’s Foundations in Quality Self-Directed Learning Program, ASQ Quality Press, 2001.

2. Nancy R. Tague, The Quality Toolbox, ASQ Quality Press, 1995.

3. ASQ, ASQ’s Foundations in Quality Self-Directed Learning Program, see reference 1.

4. Ibid.

FIGURE 1

104 I NOVEMBER 2004 I www.asq.org

My Histogram

Use a histogram to determine the amount of variation in a set of data.

FIGURE 2

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