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Look at this set of $5$ numbers: $\newline$ $73, 58, 73, 81, 40$ $\newline$ How would the mean change if the number $65$ were added to 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

73, 58, 73, 81, 40

\newline

How would the mean change if the number

65

were added to 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: $73, 58, 73, 81, 40$ $\newline$ Sum of original set = $73 + 58 + 73 + 81 + 40 = 325$ $\newline$ Number of elements in original set = $5$ $\newline$ Original mean = $\frac{325}{5} = 65$
Add Number and Recalculate Mean: Add the number $65$ to the set and calculate the new mean. $\newline$ New set: $73, 58, 73, 81, 40, 65$ $\newline$ Sum of new set = $325 + 65 = 390$ $\newline$ Number of elements in new set = $6$ $\newline$ New mean = $\frac{390}{6} = 65$
Compare Original and New Mean: Compare the original mean with the new mean. Original mean = $65$ , New mean = $65$ Since both means are equal, the mean does not change.

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