Frequency Distribution
A Frequency Distribution is simply a summary of how often each score occurs by grouping scores together.
Cannot Find This OVERHEAD: LIST OF ALL POSSIBLE SCORES/NUMBER OF OCCURRENCES
- have to group the scores so that summary makes sense
HOW:?
- group the scores into EQUAL sized intervals
- scores, not students WHY?
- Trying to find out how many students
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- A few general principles:
- decide how many groups you want
- the fewer groups, the less precise your description
- too many groups, and it's too much work, too little summary
- usually 10 to 20 groups is best
- take the range (difference between highest and lowest)
- divide by number of intervals (groups) you want
- the lowest interval (group) should begin with a number that can be divided evenly by the size of the interval width
- make sure that the lowest and highest scores are included in your table
- relationship between these depends on the frequency distribution
- Graphs
- must be clearly titled
- all symbols clearly identified
- Histogram
- vertical bar graph
- columns touch each other
Frequency distributions come in three types:
symmetrical, positively or negatively skewed
Cannot Find This OVERHEAD: THREE DISTRIBUTIONS
- If a distribution is symmetrical, the lower half of the distribution mirrors the upper half
- in symmetrical distributions, mean, median and mode will be the same (unless it is bimodal)
- In skewed distributions, median comes between mean and mode
- because mean will be dragged down or up by the few scores out on the extreme tail, while mode will hang out where the greatest action is
- If the scores are piled up at the low end, and "tail off" near the high end, it's positively skewed
- If the scores are piled up at the high end, and "tail off" near the low end, then it's negatively skewed
- Positive or Negative by the way the tail points --if tail points to high end, it's positive; if tail points towards negative end, it's negative
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