To find the mean weight of the cats, you add up all their weights and then divide by the number of cats.
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First, sum the weights: \[ 12 + 6 + 13 + 12 + 16 = 59 \]
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Next, divide the total weight by the number of cats (which is 5): \[ \text{Mean} = \frac{59}{5} = 11.8 \]
Thus, the mean weight of the cats is 11.8 pounds.