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# Measures of Central Tendency

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The mean, median, and mode are the three most common types of averages used in statistical analysis. The three are called measures of central tendency. The mode is the value that occurs most often in a data set. The median is the middle value in a set of numbers arranged in numerical order. The median is relatively unaffected by outliers because it is simply the middle number (odd list) or average of the two middle numbers (even list). The mode is also unaffected by outliers. The mean is the arithmetical average of a set of numbers (sum of numbers in the set divided by the number of numbers in the set).

Example:

In the data set, 7, 15, 2, 5, 17, 10, 8, 11, 16, 14, 8

Mode = 8 (appears twice)

Median = 10 (middle number in the arranged set: 2, 5, 7, 8, 8, 10, 11, 14, 15, 16, 17)

Mean = [(2+5+7+8+8+10+11+14+15+16+17)/11] = 10.3

Changing the datum, 17, to 51, changes the mean to 13.4; the mean is affected by outliers. The mode and the median remain unchanged.

Vic

Reference

Films Media Group. (2005). Organizing Quantitative Data. Films On Demand. Retrieved from

http://fod.infobase.com/p_ViewVideo.aspx?xtid=36200

Tokunaga, H. (2016). Fundamental statistics for the social and behavioral sciences. Sage publishing. Retrieved from https://phoenix.vitalsource.com/#/books/9781483318806/cfi/6/24[;vnd.vst.idref=ch0002]

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Here are some examples I came up with:

To get the mean, one adds up all the numbers of the set (using interval data) and then divides this total by the total number of scores. Mean can be misleading, however, if there is a large variance between the highest or lowest numbers and most of the other numbers. For instance, considering the mean to be the average would be misleading if one were using the mean to represent the typical net worth of all citizens in Washington. Bill Gates' net worth would skew the figure erroneously.

Median is the middle of the distribution, used in central tendency. The median uses ordinal or interval data, since it requires the data is put in order from high to low. Median is often chosen to describe skewed distribution and offers a precise measure of central tendency. With an odd group of numbers, this is easy to pick out. First, put the numbers in numerical order:
1, 2, 3, 3, 5, 5, 6, 7
In the numbers above, the median number is 5. If the numbers are even, one calculates the median lies halfway between the middle numbers:
1, 2, 3, 4
The median is 2.5 in the numbers above. If the middle numbers had the same value (1, 3, 3, 4), the median would be 3.
Mode is the most common number or value. It can be used with nominal, ordinal or interval data. Mode is chosen to determine central tendency when one is looking for a fast, simple measure but it is generally considered primitive. One can often see the mode by looking at a list:
Blue
Blue
Orange
Blue
Red

In this example, blue is the mode. To determine central tendency for nominal-level variables one must use mode, since there is no ranking in nominal -level variables. A frequency distribution can contain two (or even more) modes. In the example above, if blue was listed three times, orange was listed three times and red was listed twice, both blue and orange would be modes.

Tokunaga, H. (2016). Fundamental statistics for the social and behavioral sciences. Sage publishing. Retrieved from https://phoenix.vitalsource.com/#/books/9781483318806/cfi/6/24[;vnd.vst.idref=ch0002]

This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

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