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Look at this set of $8$ numbers: $\newline$ $87, 99, 29, 70, 37, 43, 15, 84$ $\newline$ How would the mean change if the number $85$ replaced the number $37$ 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

8

numbers:

\newline

87, 99, 29, 70, 37, 43, 15, 84

\newline

How would the mean change if the number

85

replaced the number

37

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Calculate Original Mean: Calculate the original mean of the set. $\newline$ Original set: $87, 99, 29, 70, 37, 43, 15, 84$ $\newline$ Sum of original set = $87 + 99 + 29 + 70 + 37 + 43 + 15 + 84 = 464$ $\newline$ Number of elements = $8$ $\newline$ Original mean = $464 / 8 = 58$
Replace and Calculate New Mean: Replace the number $37$ with $85$ in the set and calculate the new mean. $\newline$ New set: $87, 99, 29, 70, 85, 43, 15, 84$ $\newline$ Sum of new set = $87 + 99 + 29 + 70 + 85 + 43 + 15 + 84 = 512$ $\newline$ New mean = $\frac{512}{8} = 64$
Compare Original and New Mean: Compare the original mean and the new mean. Original mean = $58$ , New mean = $64$ Since $64$ is greater than $58$ , the mean increases.

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