A histogram is a graphical summary of the variation in a data set. The graphical nature of the histogram allows us to see patterns that are difficult to observe in a simple number table. This tool is used especially in the verification of theories and validity tests.
How to interpret the histograms:
We know that the values vary in every data set. This variation follows a certain pattern. The purpose of analyzing a histogram is, on the one hand, to identify and classify the pattern of variation, and on the other to develop a reasonable and relevant explanation of the pattern. The explanation should be based on general knowledge and observation of specific situations and should be confirmed by further analysis. The most common patterns of variation are bell, two-peaked, flat, comb, skewed, truncated, one-peaked, or one-tipped distribution.
Construction of a histogram:
STEP 1
Determine the range of the data: RANGE is equal to the largest data minus the smallest data; R => - <
STEP 2
Obtain in number of classes, there are several criteria to determine the number of classes (or bars). However none of them is accurate. Some authors recommend five to fifteen classes, depending on how the data is and how many there are. A frequently used criterion is that the number of classes should be approximately the square root of the number of data, for example, the square root of 30 (number of items) is greater than five, so six classes are selected.
STEP 3
Set class length: equals the range between the number of classes.
STEP 4
Construct the class intervals: The intervals result from dividing the range of the data in relation to the result of STEP 2 in equal intervals.
STEP 5
Graph the histogram: a bar graph is made, the bases of the bars are the class intervals and height is the frequency of the classes. If the midpoints of the upper base of the rectangles are joined, the frequency polygon is obtained.
Example:
At a glass container factory, a customer is demanding that the capacity of a certain type of bottle be 13 ml, with a tolerance of plus minus 1 ml. The factory establishes a quality improvement program so that the bottles that are manufactured meet the customer's requirements.
Example of a Histogram
Examples of other types of graphic representations:
There are histograms where the data is grouped into classes, and we count how many observations (absolute frequency) there are in each of them. In some variables (qualitative variables) the classes are defined in a natural way, eg sex with two classes: female, male or blood group with four: A, B, AB, O. In the quantitative variables, the classes must be explicitly defined (class intervals).
Simple Histogram
The class intervals are represented on the abscissa axis (horizontal axis) and the frequencies, absolute or relative, on the ordinate axis (vertical axis).
Cumulative Histogram
Sometimes it is more useful to represent the accumulated frequencies.
Histogram by Groups
Or simultaneously represent the histograms of one variable in two different situations.
Directed Histogram
Another very common way of representing two histograms of the same variable in two different situations.
Stratified Histogram
Another way.
Cumulative Warhead - Histograms
In the ordinal quantitative or qualitative variables, frequency polygons can be represented instead of histograms, when the cumulative frequency is represented, it is called a warhead.
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