The mean of 12 numbers is 18. If one number 30 is replaced by 6, find the new mean.
16
Mean = sum of the numbers ÷ count, so the sum of the 12 numbers = 12 × 18 = 216.
Replacing 30 by 6 lowers the sum by 30 – 6 = 24, so the new sum = 216 – 24 = 192, while the count stays 12.
New mean = \(\frac{192}{12} = 16\).
Check: the mean falls by \(\frac{24}{12} = 2\), and 18 – 2 = 16, which agrees with the direct calculation.
Hence, 16.
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