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Fundamentals of Statistics 1: Basic Concepts :: Describing the Center of Data
When data are quantitative we often want to summarize the middle or most typical value. We usually refer to this as the average. In statistics we need to be a bit more precises though as there are several averages: mean, median, mode, geometric mean, harmonic mean, winzorized mean, trimmed mean etc.

The one we should be most familiar with is the arithmetic mean. This is the sum of all the data divided by the number of values in the data.



The median is the mid-point of a set of data and is a better measure of the center of data when the data are skewed by large or small values. Sales price of homes, salaries of employees are examples of positively skewed data. The mean is heavily influenced by one large value, whereas the median is not.

The mode represents the most frequent value in a set of data. For example in the set of data: 3,5,6,7,7,9,8,7,5,6,4,5,3,1 the number 7 is the mode. The mode doesn't have to be the center of a set of data and there can be more than one mode.

I've analyzed a lot of data, and in my experience I use the mean about 75% of the time, then median about 14% of the time, other means like the geometric mean about 10% of the time and the mode less than 1% of the time.  So get to know the mean--it's your friend.

There is a lot to say about measures of the center (central tendency). See Huff's excellent book on How to Lie with Statistics. It was written over 50 years ago but is still relevant today. It is full of examples to better equip you with interpreting and using measures of central tendency.

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