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Look at this set of 88 numbers:\newline5,4,9,2,6,7,7,85, 4, 9, 2, 6, 7, 7, 8\newlineHow would the mean change if the number 11 replaced the number 99 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 88 numbers:\newline5,4,9,2,6,7,7,85, 4, 9, 2, 6, 7, 7, 8\newlineHow would the mean change if the number 11 replaced the number 99 in the set?\newlineChoices:\newline(A)increase\newline(B)decrease\newline(C)no change
  1. Calculate Original Mean: Calculate the mean of the original set.\newlineOriginal set: 5,4,9,2,6,7,7,85, 4, 9, 2, 6, 7, 7, 8\newlineSum of original set = 5+4+9+2+6+7+7+8=485 + 4 + 9 + 2 + 6 + 7 + 7 + 8 = 48\newlineNumber of elements = 88\newlineOriginal mean = 488=6\frac{48}{8} = 6
  2. Calculate New Mean: Calculate the mean of the new set after replacing 99 with 11.\newlineNew set: 5,4,1,2,6,7,7,85, 4, 1, 2, 6, 7, 7, 8\newlineSum of new set = 5+4+1+2+6+7+7+8=405 + 4 + 1 + 2 + 6 + 7 + 7 + 8 = 40\newlineNumber of elements = 88\newlineNew mean = 40/8=540 / 8 = 5
  3. Compare Means: Compare the original mean and the new mean.\newlineOriginal mean = 66\newlineNew mean = 55\newlineSince 55 is less than 66, the mean decreases.

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