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Look at this set of 99 numbers:\newline21,44,17,53,97,80,56,63,9121, 44, 17, 53, 97, 80, 56, 63, 91\newlineHow would the mean change if the number 9090 replaced the number 6363 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 99 numbers:\newline21,44,17,53,97,80,56,63,9121, 44, 17, 53, 97, 80, 56, 63, 91\newlineHow would the mean change if the number 9090 replaced the number 6363 in the set?\newlineChoices:\newline(A)increase\newline(B)decrease\newline(C)no change
  1. Calculate Original Mean: Step 11: Calculate the original mean of the set.\newlineOriginal set: 21,44,17,53,97,80,56,63,9121, 44, 17, 53, 97, 80, 56, 63, 91\newlineSum of original set = 21+44+17+53+97+80+56+63+91=52221 + 44 + 17 + 53 + 97 + 80 + 56 + 63 + 91 = 522\newlineNumber of elements = 99\newlineOriginal mean = 522/9=58522 / 9 = 58
  2. Calculate New Mean: Step 22: Calculate the new mean after replacing 6363 with 9090.\newlineNew set: 21,44,17,53,97,80,56,90,9121, 44, 17, 53, 97, 80, 56, 90, 91\newlineSum of new set = 21+44+17+53+97+80+56+90+91=54921 + 44 + 17 + 53 + 97 + 80 + 56 + 90 + 91 = 549\newlineNumber of elements = 99\newlineNew mean = 549/9=61549 / 9 = 61
  3. Compare Means: Step 33: Compare the original mean and the new mean.\newlineOriginal mean = 5858\newlineNew mean = 6161\newlineSince 61 > 58, the mean increases.

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