Histogram

Components of a Histogram

Histograms typically include the following elements:

• An x-axis divided into bars (intervals) for the observed values of the variable
• A y-axis representing the frequency that observed values fall within each bin
• Vertical Bars representing frequencies
• Optionally, a superimposed fitted distribution

Where it helps:

• Highlight the central tendency of the data
• Emphasize the variability of the data
• Determine whether a sample distribution is symmetrical or skewed

 

Characteristics

• A histogram is an accurate representation of the distribution of numerical data.
• It is an estimate of the probability distribution of a continuous variable and was first introduced by Karl Pearson.
• It differs from a bar graph, in the sense that a bar graph relates two variables, but a histogram relates only one.
• As the adjacent bins leave no gaps, the rectangles of a histogram touch each other to indicate that the original variable is continuous
• The higher that the bar is, the greater the frequency of data values in that bin.Use histograms to visualize the distribution of sample data. Look at the central tendency, variation, and overall shape of the distribution. You might create a histogram before or during an analysis to help confirm assumptions and guide further analysis.

 

Histograms are based on area of bars, not only the height of bars

In a histogram, it is the area of the bar that indicates the frequency of occurrences for each bin in association with the height. 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 (bins), and under these circumstances, the height of the bin does reflect the frequency.

Difference between a bar chart and a histogram

The major difference between a histogram and a bar chart is that a histogram is only used to depict the frequency of occurrences of data points 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.

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). 

When Are Histograms Used?

• Summarize large data sets graphically
• Compare measurements to specifications
• Communicate information to the team
• Assist in decision making