Understanding Histograms And Bar Graphs
Every business does its best to minimize variation in its products and services by taking careful stock of what’s produced and looking for trends. But presenting these measurements as statistics doesn’t reveal business operations as effectively as the graphical representation of a histogram. Join hosts Jennifer Scarborough and James Fletcher for a lesson in making business management easy on the eyes.
A histogram lives up to the old adage that a picture is worth a thousand words. It is a frequency distribution graph that emphasizes variations in the measurements of nearly identical things. The horizontal axis of a histogram shows what is being measured; the vertical axis shows how frequently each value occurs. When you think of histograms, you’re likely to think of a graph showing several side-by-side columns, the heights of which delineate a bell-shaped curve.
Every histogram is constructed to illustrate the result of one and only one kind of measurement – weight, for example. Say a factory that produces bars of soap calibrates its machines so the majority of bars will weigh 103 grams. If a random sample of 50 bars produced is examined, the largest portion of them should weigh 103 grams. These bars can be stacked in one tall column, as shown in the image below. Some bars weigh 104 grams and are stacked just next to the column of bars weighing 103 grams. A few bars weigh 105 grams and go just to the right of the bars weighing 104 grams. Two bars weigh 106 grams and are stacked to the extreme right of the others. When bars weighing less than the expected 103 grams are similarly stacked on the left side of the 103-gram column, the general form of a histogram becomes evident.
There are three general types of histograms that you’re likely to see. A normal curve is bell-shaped, as in the example of the stacked bars of soap. The skewed histogram is lopsided, because most of its distribution is off to one side. The bimodal histogram is made up of two curves.
Business Management Data
Customers expect consistency. In a factory where the processes remain the same, there should be a lot of look-alikes in a product sample. When look-alikes aren’t being produced, it signals the need to investigate.
In business management, the average value of most histograms should lie at the center of the specification limits. Returning to the soap example, if the labels on those bars of soap say the bars contain 100 grams, the minimum acceptable weight must be set at 100 grams. Theoretically, the maximum could be quite high – the customer would never complain (though this would be unnecessarily costly for the producer).
A sudden, unexplained broadening of a histogram would be a candidate for cause-and-effect analysis. Imagine six boards placed side by side and cut in the shape of a normally distributed, bell-shaped histogram. Each board represents a standard deviation. The two center pieces represent approximately 68 percent of the sample. The two pieces adjacent to the center pieces represent approximately 27 percent of the sample. Less than 5 percent of the sample is represented by the two pieces at the edge of the acceptable range. It should be rare for any portion of a sample to fall along the trailing edges of the histogram. Tiny wedges on each side of the row of boards could represent these unacceptable deviations, which would indicate the need for adjustments in production.
When the width of the histogram suddenly narrows, what action should be taken? Use cause-and-effect analysis to find out why, so production can be kept that way. In business presentations, the improved or ideal situation is sometimes presented as a narrowed histogram superimposed (as a dotted and/or colored line) over the histogram that illustrates an undesirable condition.
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