Complete The Class Limits And Class Boundaries Columns

Complete The Class Limits And Class Boundaries Columns Of The Distribu

Complete The Class Limits And Class Boundaries Columns Of The Distribu

Complete the class limits and class boundaries columns of the distribution table below given the following information: the smallest value is 54 and the largest value is 105. The data will be divided into seven classes. Enter your responses in the space provided.

Class Limits Class Boundaries

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The task involves completing the class limits and class boundaries in a frequency distribution table based on the data range from 54 to 105, divided into seven classes. To accurately determine these, the first step is to calculate the class width, which is essential for constructing class intervals.

Calculating the class width: subtract the minimum value from the maximum value and divide by the number of classes. That is, (105 - 54) / 7 = 51 / 7 ≈ 7.29. Since class widths are typically rounded to a convenient number, we might choose 7 or 8 for simplicity. Choosing a class width of 8 ensures all data are covered without gaps, and the classes will be neat and easy to interpret.

Using a class width of 8, the classes would start at or below 54, with the upper limit of the first class at 61 (since 54 + 8 - 1 = 61). The subsequent class limits can be calculated by adding the class width to the lower limit of each subsequent class.

Therefore, the class limits are as follows:

  • Class 1: Lower limit = 54, Upper limit = 61
  • Class 2: Lower limit = 62, Upper limit = 69
  • Class 3: Lower limit = 70, Upper limit = 77
  • Class 4: Lower limit = 78, Upper limit = 85
  • Class 5: Lower limit = 86, Upper limit = 93
  • Class 6: Lower limit = 94, Upper limit = 101
  • Class 7: Lower limit = 102, Upper limit = 109

Note that the last class extends slightly beyond the maximum value of 105 to ensure all data points are included. Alternatively, if the precise maximum value is 105, the last class's upper limit can be set to 105, adjusting the earlier classes accordingly.

Now, to determine the class boundaries, which are used to avoid gaps between classes and for graphical representation, subtract 0.5 from each lower class limit and add 0.5 to each upper class limit:

  • Class 1: 54 - 0.5 = 53.5, 61 + 0.5 = 61.5
  • Class 2: 62 - 0.5 = 61.5, 69 + 0.5 = 69.5
  • Class 3: 70 - 0.5 = 69.5, 77 + 0.5 = 77.5
  • Class 4: 78 - 0.5 = 77.5, 85 + 0.5 = 85.5
  • Class 5: 86 - 0.5 = 85.5, 93 + 0.5 = 93.5
  • Class 6: 94 - 0.5 = 93.5, 101 + 0.5 = 101.5
  • Class 7: 102 - 0.5 = 101.5, 109 + 0.5 = 109.5

This method ensures that data points equal to class boundaries are included in the appropriate classes without overlapping gaps. Properly calculating class limits and boundaries is crucial in statistical analysis for clarity in data presentation and ease of interpretation.

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