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Look at this set of 77 numbers:\newline68,84,25,52,68,18,7068, 84, 25, 52, 68, 18, 70\newlineHow would the mean change if the number 7070 replaced the number 8484 in the set?\newlineChoices:\newline(A)increase\newline(B)decrease\newline(C)no change

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Full solution

Q. Look at this set of 77 numbers:\newline68,84,25,52,68,18,7068, 84, 25, 52, 68, 18, 70\newlineHow would the mean change if the number 7070 replaced the number 8484 in the set?\newlineChoices:\newline(A)increase\newline(B)decrease\newline(C)no change
  1. Calculate Original Mean: Calculate the original mean of the set: 68,84,25,52,68,18,7068, 84, 25, 52, 68, 18, 70. \newlineSum of original set = 68+84+25+52+68+18+70=38568 + 84 + 25 + 52 + 68 + 18 + 70 = 385\newlineNumber of elements = 77\newlineOriginal mean = 385/7=55385 / 7 = 55
  2. Calculate New Mean: Calculate the new mean after replacing 8484 with 7070.\newline New set = 68,70,25,52,68,18,7068, 70, 25, 52, 68, 18, 70\newline Sum of new set = 68+70+25+52+68+18+70=37168 + 70 + 25 + 52 + 68 + 18 + 70 = 371\newline New mean = 371/7=53371 / 7 = 53
  3. Compare Means: Compare the original mean and the new mean to determine the change.\newlineOriginal mean = 5555\newlineNew mean = 5353\newlineSince 5353 is less than 5555, the mean decreases.

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