How to Construct a Grouped Frequency Distribution Chart Using Classes

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Grouped frequency distribution charts let statisticians organize large sets of data in a format that is easy to comprehend. For instance, if 10 students scored an A, 30 students scored a B and five students scored a C, you could represent this large set of data in a frequency distribution chart. The most common type of frequency distribution chart is a histogram, which is a specialized bar graph, wherein the data is divided by adjacent intervals of equal length known as classes.

Things You'll Need

  • paper
  • pencil
  • Determine the number of classes. Typically, the number of classes chosen is a value between 5 and 20. For the purpose of an example, opt for five classes.

  • Calculate the class width by subtracting the highest value by the lowest value, dividing the result by the number of classes and rounding up. Assume the following data set pertaining to student scores from an exam with 100 possible points:

    54
    40
    86
    84
    92
    75
    85
    92
    45
    89
    94
    68
    78
    84

    Subtract the highest value (94) by the lowest value (40) to get 54. Divide 54 by the number of classes (5) to obtain 10.8. Round 10.8 up to 11.

  • Select the lower limit of the first class. Some choose the lowest score while others opt for a more convenient value that is lower (not higher). Given the example, set the lowest limit to 40.

  • Add the class width to the lower limit of the first class to calculate the upper limit of the first class and the lower limit of the next class. Continue until all classes are completed. Given the example, add 11 to 40 to get the first class (40 - 41) and continue as follows:

    (40 - 51)
    (51 - 62)
    (62 - 73)
    (73 - 84)
    (84 - 95)

  • Determine the frequencies for each class by counting the number of data values that fit for each class. The total frequency value should be equal to the total number of data values. Given the student scores:

    (40 - 51): 2
    (51 - 62): 1
    (62 - 73): 1
    (73 - 84): 2
    (84 - 95): 8

  • Create a grouped frequency distribution histogram cart by drawing a bar graph where each bar's height is a frequency value, each bar's width is a class and all of the bars are adjacent to one another. Given the example, the widths are 40 - 51, 51 - 62, 62 - 73, 73 - 84 and 84 - 95, while the heights are 2, 1, 1, 2 and 8.

Tips & Warnings

  • Usually, the number of classes is given. If it isn't a number between 5 and 10 will work well most of the time.

References

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