A histogram is a type of graph that has wide applications in statistics. Histograms provide a visual interpretation of numerical data by indicating the number of data points that lie within a range of values. These ranges of values are called classes or bins. The frequency of the data that falls in each class is depicted by the use of a bar. The higher that the bar is, the greater the frequency of data values in that bin.

At first glance, histograms look very similar to bar graphs. Both graphs employ vertical bars to represent data. The height of a bar corresponds to the relative frequency of the amount of data in the class. The higher the bar, the higher the frequency of the data.

The lower the bar, the lower the frequency of data. But looks can be deceiving. It is here that the similarities end between the two kinds of graphs.

The reason that these kinds of graphs are different has to do with the level of measurement of the data. On one hand, bar graphs are used for data at the nominal level of measurement.

Bar graphs measure the frequency of categorical data, and the classes for a bar graph are these categories. On the other hand, histograms are used for data that is at least at the ordinal level of measurement. The classes for a histogram are ranges of values. Another key difference between bar graphs and histograms has to do with the ordering of the bars. In a bar graph, it is common practice to rearrange the bars in order of decreasing height. However, the bars in a histogram cannot be rearranged.A frequency distribution shows how often each different value in a set of data occurs.

A histogram is the most commonly used graph to show frequency distributions. It looks very much like a bar chart, but there are important differences between them. Start by tracking the defects on the check sheet. The tool will create a histogram using the data you enter.

A common pattern is the bell-shaped curve known as the "normal distribution. Note that other distributions look similar to the normal distribution. Statistical calculations must be used to prove a normal distribution. It's important to note that "normal" refers to the typical distribution for a particular process. For example, many processes have a natural limit on one side and will produce skewed distributions.

The skewed distribution is asymmetrical because a natural limit prevents outcomes on one side. For example, a distribution of analyses of a very pure product would be skewed, because the product cannot be more than percent pure. Other examples of natural limits are holes that cannot be smaller than the diameter of the drill bit or call-handling times that cannot be less than zero.

These distributions are called right- or left-skewed according to the direction of the tail. The bimodal distribution looks like the back of a two-humped camel. The outcomes of two processes with different distributions are combined in one set of data. For example, a distribution of production data from a two-shift operation might be bimodal, if each shift produces a different distribution of results.

Stratification often reveals this problem. Because there are many peaks close together, the top of the distribution resembles a plateau. The edge peak distribution looks like the normal distribution except that it has a large peak at one tail.

In a comb distribution, the bars are alternately tall and short. For example, temperature data rounded off to the nearest 0. The truncated distribution looks like a normal distribution with the tails cut off. The supplier might be producing a normal distribution of material and then relying on inspection to separate what is within specification limits from what is out of spec. The resulting shipments to the customer from inside the specifications are the heart cut.

The dog food distribution is missing something—results near the average. Even though what the customer receives is within specifications, the product falls into two clusters: one near the upper specification limit and one near the lower specification limit.

## What Is a Histogram?

About Histogram. Histogram Resources. Histogram Related Topics. Looking for more quality tools? Featured Advertisers.You can see for example that there are 30 trees from cm to just below cm tall.

Notice that the horizontal axis is continuous like a number line :. Histograms are a great way to show results of continuous datasuch as:. A Frequency Histogram is a special graph that uses vertical columns to show frequencies how many times each score occurs :. Histogram : a graphical display of data using bars of different heights. Example: Height of Orange Trees You measure the height of every tree in the orchard in centimeters cm The heights vary from cm to cm You decide to put the results into groups of 50 cm: The to just below cm range, The to just below cm range, etc So a tree that is cm tall is added to the "" range.

And here is the result: You can see for example that there are 30 trees from cm to just below cm tall PS: you can create graphs like that using Make your own Histogram. Example: How much is that puppy growing? Each month you measure how much weight your pup has gained and get these results: 0. And here is the result: There are no values from 1 to just below 1.

Here I have added up how often 1 occurs 2 timeshow often 2 occurs 5 timesetc, and shown them as a histogram.Topics: LearningStatisticsStats. Histograms are one of the most common graphs used to display numeric data. Anyone who takes a statistics course is likely to learn about the histogram, and for good reason: histograms are easy to understand and can instantly tell you a lot about your data.

If the left side of a histogram resembles a mirror image of the right side, then the data are said to be symmetric. In this case, the mean or average is a good approximation for the center of the data. And we can therefore safely utilize statistical tools that use the mean to analyze our data, such as t-tests.

If the data are not symmetric, then the data are either left-skewed or right-skewed. If the data are skewed, then the mean may not provide a good estimate for the center of the data and represent where most of the data fall. In this case, you should consider using the median to evaluate the center of the data, rather than the mean.

However, you can still observe an approximation for the range and see how spread out the data are. And you can answer questions such as "Is there a little bit of variability in my organization's salaries, or a lot? Outliers can be described as extremely low or high values that do not fall near any other data points.

Sometimes outliers represent unusual cases. Other times they represent data entry errors, or perhaps data that does not belong with the other data of interest. Whatever the case may be, outliers can easily be identified using a histogram and should be investigated as they can shed interesting information about your data.

### Histograms Introduction

Rewind to the mids when scientists reported depleting ozone levels above Antarctica. The analysis they used automatically eliminated any Dobson readings below units because ozone levels that low were thought to be impossible. Minitab is the leading provider of software and services for quality improvement and statistics education. Minitab LLC. Our global network of representatives serves more than 40 countries around the world. The Minitab Blog. Search for a blog post:. Here are three of the most important things you can learn by looking at a histogram. Shape—Mirror, Mirror, On the Wall… If the left side of a histogram resembles a mirror image of the right side, then the data are said to be symmetric. Did you know Span—A Little or a Lot? Who We Are Minitab is the leading provider of software and services for quality improvement and statistics education.A histogram is a plot that lets you discover, and show, the underlying frequency distribution shape of a set of continuous data.

This allows the inspection of the data for its underlying distribution e. An example of a histogram, and the raw data it was constructed from, is shown below:. To construct a histogram from a continuous variable you first need to split the data into intervals, called bins.

In the example above, age has been split into bins, with each bin representing a year period starting at 20 years. Each bin contains the number of occurrences of scores in the data set that are contained within that bin. For the above data set, the frequencies in each bin have been tabulated along with the scores that contributed to the frequency in each bin see below :.

Bin Frequency Scores Included in Bin 2 25,22 4 36,38,36,38 4 46,45,48,46 5 55,55,52,58,55 3 68,67,61 1 72 0 - 1 Notice that, unlike a bar chart, there are no "gaps" between the bars although some bars might be "absent" reflecting no frequencies. This is because a histogram represents a continuous data set, and as such, there are no gaps in the data although you will have to decide whether you round up or round down scores on the boundaries of bins.

There is no right or wrong answer as to how wide a bin should be, but there are rules of thumb. You need to make sure that the bins are not too small or too large. Consider the histogram we produced earlier see above : the following histograms use the same data, but have either much smaller or larger bins, as shown below:.

We can see from the histogram on the left that the bin width is too small because it shows too much individual data and does not allow the underlying pattern frequency distribution of the data to be easily seen. At the other end of the scale is the diagram on the right, where the bins are too large, and again, we are unable to find the underlying trend in the data.

### Understanding Histograms

In a histogram, it is the area of the bar that indicates the frequency of occurrences for each bin. This means that the height of the bar does not necessarily indicate how many occurrences of scores there were within each individual bin. It is the product of height multiplied by the width of the bin that indicates the frequency of occurrences within that bin. One of the reasons that the height of the bars is often incorrectly assessed as indicating frequency and not the area of the bar is due to the fact that a lot of histograms often have equally spaced bars binsand under these circumstances, the height of the bin does reflect the frequency.

The major difference is that a histogram is only used to plot the frequency of score occurrences in a continuous data set that has been divided into classes, called bins.

Bar charts, on the other hand, can be used for a great deal of other types of variables including ordinal and nominal data sets. Histograms What is a histogram? An example of a histogram, and the raw data it was constructed from, is shown below: 36 25 38 46 55 68 72 55 36 38 67 45 22 48 91 46 52 61 58 55 How do you construct a histogram from a continuous variable? For the above data set, the frequencies in each bin have been tabulated along with the scores that contributed to the frequency in each bin see below : Bin Frequency Scores Included in Bin 2 25,22 4 36,38,36,38 4 46,45,48,46 5 55,55,52,58,55 3 68,67,61 1 72 0 - 1 91 Notice that, unlike a bar chart, there are no "gaps" between the bars although some bars might be "absent" reflecting no frequencies.

Join the 10,s of students, academics and professionals who rely on Laerd Statistics. Choosing the correct bin width There is no right or wrong answer as to how wide a bin should be, but there are rules of thumb.A histogram is an approximate representation of the distribution of numerical or categorical data. It was first introduced by Karl Pearson. The bins are usually specified as consecutive, non-overlapping intervals of a variable.

The bins intervals must be adjacent, and are often but not required to be of equal size. If the bins are of equal size, a rectangle is erected over the bin with height proportional to the frequency —the number of cases in each bin. A histogram may also be normalized to display "relative" frequencies. It then shows the proportion of cases that fall into each of several categorieswith the sum of the heights equaling 1.

However, bins need not be of equal width; in that case, the erected rectangle is defined to have its area proportional to the frequency of cases in the bin. Examples of variable bin width are displayed on Census bureau data below. As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous.

Histograms give a rough sense of the density of the underlying distribution of the data, and often for density estimation : estimating the probability density function of the underlying variable. The total area of a histogram used for probability density is always normalized to 1. If the length of the intervals on the x -axis are all 1, then a histogram is identical to a relative frequency plot.

A histogram can be thought of as a simplistic kernel density estimationwhich uses a kernel to smooth frequencies over the bins. This yields a smoother probability density function, which will in general more accurately reflect distribution of the underlying variable. The density estimate could be plotted as an alternative to the histogram, and is usually drawn as a curve rather than a set of boxes. Histograms are nevertheless preferred in applications, when their statistical properties need to be modeled.

The correlated variation of a kernel density estimate is very difficult to describe mathematically, while it is simple for a histogram where each bin varies independently. An alternative to kernel density estimation is the average shifted histogram,  which is fast to compute and gives a smooth curve estimate of the density without using kernels.

The histogram is one of the seven basic tools of quality control. Histograms are sometimes confused with bar charts.What is it and should I take any notice of it? Is there such a thing as the ideal histogram?

What is a Frequency Polygon?

What should we be aiming for? Histograms are a topic that we could and probably should spend a lot of time talking about but let me give you a very brief answer to get you through in the short term. Histograms are a very useful tool that many cameras offer their users to help them get a quick summary of the tonal range present in any given image.

The higher the graph at any given point the more pixels of that tone that are present in an image. So a histogram with lots of dark pixels will be skewed to the left and one with lots of lighter tones will be skewed to the right.

The above shot has a lot of light tones — in fact there are parts of the shot that are quite blown out. As a result on the right hand side of the histogram you can see a sudden rise. While there are quite a few mid tones — everything is skewed right and with the extreme values on the right hand side indicate an over exposed shot. This second shot has a lot of dark tones.

The resulting histogram is quite different to the first one — the values are skewed to the left hand side. For example taking a silhouette shot might produce a histogram with peaks at both ends of the spectrum and nothing much in the middle of the graph. Taking a shot of someone at the snow will obviously have a histogram with significant peaks on the right hand side…. Most well exposed shots tend to peak somewhere in the middle and taper off towards the edges.

This will enable you to see both the picture and the histogram when reviewing shots after taking them. Keep an eye out for histograms with dramatic spikes to the extreme ends of either side of the spectrum. This indicates that you have a lot of pixels that are either pure black or pure white.

The histogram is really just a tool to give you more information about an image and to help you get the effect that you want. Having your camera set to show you histograms during the view process will tell you how your image is exposed. You can see in this shot a much more even spread of tones.