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Central Tendency, The mode is very flexible in how it can be described! -…
Central Tendency
Mean: The arithmetic average of the data. The sum of all scores divided by the number of scores reported.
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Weighted Mean: A mean that combines two (or more) sets of scores and finds the mean of them combined, weighting each based on sample size.
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Changing the Mean
Changing Scores: Because changing scores changes the sum of all scores, it will change the mean in the same direction.
Adding or Removing Scores: This will also change the sum of all scores, so it will also change the mean, unless the new score added is the same as the previous mean. Adding a number higher or lower than the mean will increase or decrease it, while removing a number higher or lower than the mean will decrease or increase it, respectively.
Uniformly Changing Scores: If you uniformly perform an operation on each of the scores, the mean will change by the same operation. For instance, if you multiply each score by 3, the mean will also be multiplied by 3.
The mean, median and mode will be the same for a perfectly symmetrical distribution, and close together if the distribution is symmetrical, but not perfectly. Though, if the distribution is bi- or multi-modal the modes will instead be to each side of the mean and median.
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Median: The midpoint of the distribution, where 50% of the scores are higher and 50% of the scores are lower
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The median defines the center of the distribution in terms of scores, rather than distance.
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Data can have a median if it is numerical or ordinal (like grade level), where the mean can only be calculated using numerical data sets.
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Which to use?
Generally, the mean is the best representative of central tendency for numerical data.
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