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Understanding Histograms: Visualizing Frequency Distributions in Data Sets

A histogram is a graphical representation that displays the frequency distribution of numerical data. For example, given the set {1,2,2,3,3,3,3,4,4,5,6}, we can create a histogram to visualize the frequency of each number. In real-world data, many numbers may be unique, making it necessary to use ranges for effective representation. A well-defined peak in a histogram indicates a significant answer, while low peaks suggest less importance. Analyzing these peaks can provide insights into the occurrence range and underlying patterns of the data.

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Understanding Histograms: Visualizing Frequency Distributions in Data Sets

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  1. What is a Histogram?SHOWS FREQUENCYThus if we have the set {1,2,2,3,3,3,3,4,4,5,6}, we can graph them like this:

  2. Other Histograms

  3. In most real data sets almost all numbers will be unique. Consider the set {3, 11, 12, 19, 22, 23, 24, 25, 27, 29, 35, 36, 37, 38, 45, 49} • Instead, USE A RANGE

  4. The higher the peak, the more likely that is the “answer” Well defined peak…low peaks insignificant

  5. What does this histogram tell you? Fairly close peak…less defined. Can determine a range of occurrence.

  6. What does this peak tell you? No ONE definite peak….no definite answer

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