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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Solution Summary
This solution explains and gives examples of measures of central tendency (mean,mode, and median). Includes APA formatted reference.
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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 ...
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