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Look at this set of $5$ numbers: $\newline$ $80, 95, 69, 80, 46$ $\newline$ How would the mean change if the number $71$ replaced the number $46$ in the set? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease $\newline$ (C)no change

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Changes in mean, median, mode, and range

Full solution

Q. Look at this set of

5

numbers:

\newline

80, 95, 69, 80, 46

\newline

How would the mean change if the number

71

replaced the number

46

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Calculate original mean: Step $1$ : Calculate the original mean of the set. $\newline$ Original set: $80, 95, 69, 80, 46$ $\newline$ Sum of original set = $80 + 95 + 69 + 80 + 46 = 370$ $\newline$ Number of elements = $5$ $\newline$ Original mean = $370 / 5 = 74$
Replace number and calculate new mean: Step $2$ : Replace the number $46$ with $71$ in the set and calculate the new mean. $\newline$ New set: $80, 95, 69, 80, 71$ $\newline$ Sum of new set = $80 + 95 + 69 + 80 + 71 = 395$ $\newline$ New mean = $\frac{395}{5} = 79$
Compare original and new mean: Step $3$ : Compare the original mean and the new mean to determine the change. $\newline$ Original mean = $74$ $\newline$ New mean = $79$ $\newline$ Since 79 > 74, the mean increases.

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