Monday, February 9, 2009

Measures of Central Tendency in Numerical Data

Measuring central tendency in a distribution of data(numbers) provides a one-digit statistic, or descriptive source of information, that convey a lot of information about that data.

It is not as complicated as it sounds, consider the three most common ways of measuring central tendency: mean(average),median, and mode.

Consider a set of numerical data {1,3,4,5,5,6,6,7,8,10) N=10
Capital N is commonly used to represent the total number in the set(population) of data(the sample).

The mean, or average, is found by adding all elements of the data and then dividing by the total number in the set.

mean = 1+3+4+5+5+6+6+7+8+10/10 = 55/10 = 5.5
So the mean or average is 5.5

The median is found by ordering the numbers from lowest to highest and locating the value in the middle.
In this case, both 5 and 6 are in the middle, thus the median is the average of the two or 5+6/2 = 5.5

The mode is the most frequent value in the data set. For our example set it both 5 and 6 appear twice, and thus, they are both the mode.

It is no accident that the mean, median, and mode produce numbers which are either equal or close. Measures of central tendency are similar, after all the number which appears most (mode) is expected to most affect the average.

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