One property of the mean is that if we know the means and sample sizes of two (or more) data sets, we can calculate the combined mean of both (or all) data sets. The combined mean for two data sets is calculated by using the formula

Where n1 and n2 are the sample sizes of the two data sets and 1 and 2 are the means of the two data sets, respectively. Suppose a sample of 10 statistics books gave a mean price of $140 and a sample of 8 mathematics books gave a mean price of $160. Find the combined mean.

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Combined mean = x = nntn2r, n 12