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Center of a data set: mean, median, mode - Measures of Central Tendency

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Center of a data set: mean, median, mode

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Notes:
3 ways for describing the “center” of a data set:

1. mean (x\overline{x} or μ\mu): arithmetic average of a data set

x=x1+x2...+xnn\overline{x}= \frac{x_1+x_2...+x_n}{n}
xx: data value
nn: # of items in a data set

2. median: the “middle” of a sorted list of data values



3. mode: the data value that occurs most often in a data set

\cdot The median is not affected by outliers, but the mean is.

\cdot weighted mean(xweighted\overline{x}_{weighted}): arithmetic average where some data values contribute more than others

xweighted=\overline{x}_{weighted}= i=1nxiwii=1nwi\frac{\sum_{{i=1}}^{n}x_i \cdot w_i}{\sum_{{i=1}}^{n}w_i}

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Center of a data set: mean, median, mode

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