Central Tendency

Normal distribution, Mean, Logarithm

Central Tendency

Central Tendency Definition:
A measure of central tendency is a measure that tells us where the middle of a bunch of data lies. The three most common measures of central tendency are the mean, the median, and the mode.

Measures of central tendency are measures of the location of the middle or the center of a distribution. The definition of "middle" or "center" is purposely left somewhat vague so that the term "central tendency" can refer to a wide variety of measures. The mean is the most commonly used measure of central tendency. The following measures of central tendency are discussed in this text:

1. Mean
2. Median
3. Mode
4. Trimean
5. Trimmed mean

Arithmetic Mean
The arithmetic mean is what is commonly called the average: When the word "mean" is used without a modifier, it can be assumed that it refers to the arithmetic mean. The mean is the sum of all the scores divided by the number of scores. The formula in summation notation is:

μ = ΣX/N

where μ is the population mean and N is the number of scores.

If the scores are from a sample, then the symbol M refers to the mean and N refers to the sample size. The formula for M is the same as the formula for μ.

M = ΣX/N

The mean is a good measure of central tendency for roughly symmetric distributions but can be misleading in skewed distributions since it can be greatly influenced by scores in the tail. Therefore, other statistics such as the median may be more informative for distributions such as reaction time or family income that are frequently very skewed

Click here for an interactive demonstration of properties of the mean and median.

The sum of squared deviations of scores from their mean is lower than their squared deviations from any other number.

For normal distributions, the mean is the most efficient and therefore the least subject to sample fluctuations of all measures of central tendency.

The formal definition of the arithmetic mean...
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