Statistics: Grouped Frequency Distributions

Guidelines for classes

  1. There should be between 5 and 20 classes.
  2. The class width should be an odd number. This will guarantee that the class midpoints are integers instead of decimals.
  3. The classes must be mutually exclusive. This means that no data value can fall into two different classes
  4. The classes must be all inclusive or exhaustive. This means that all data values must be included.
  5. The classes must be continuous. There are no gaps in a frequency distribution. Classes that have no values in them must be included (unless it's the first or last class which are dropped).
  6. The classes must be equal in width. The exception here is the first or last class. It is possible to have an "below ..." or "... and above" class. This is often used with ages.

Creating a Grouped Frequency Distribution

  1. Find the largest and smallest values
  2. Compute the Range = Maximum - Minimum
  3. Select the number of classes desired. This is usually between 5 and 20.
  4. Find the class width by dividing the range by the number of classes and rounding up. There are two things to be careful of here. You must round up, not off. Normally 3.2 would round to be 3, but in rounding up, it becomes 4. If the range divided by the number of classes gives an integer value (no remainder), then you can either add one to the number of classes or add one to the class width. Sometimes you're locked into a certain number of classes because of the instructions. The Bluman text fails to mention the case when there is no remainder.
  5. Pick a suitable starting point less than or equal to the minimum value. You will be able to cover: "the class width times the number of classes" values. You need to cover one more value than the range. Follow this rule and you'll be okay: The starting point plus the number of classes times the class width must be greater than the maximum value. Your starting point is the lower limit of the first class. Continue to add the class width to this lower limit to get the rest of the lower limits.
  6. To find the upper limit of the first class, subtract one from the lower limit of the second class. Then continue to add the class width to this upper limit to find the rest of the upper limits.
  7. Find the boundaries by subtracting 0.5 units from the lower limits and adding 0.5 units from the upper limits. The boundaries are also half-way between the upper limit of one class and the lower limit of the next class. Depending on what you're trying to accomplish, it may not be necessary to find the boundaries.
  8. Tally the data.
  9. Find the frequencies.
  10. Find the cumulative frequencies. Depending on what you're trying to accomplish, it may not be necessary to find the cumulative frequencies.
  11. If necessary, find the relative frequencies and/or relative cumulative frequencies.

It is possible to have the TI-82 calculator find the frequencies for you. You will have to find the class width and class boundaries first.

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