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Look at this set of $9$ numbers: $\newline$ $93, 69, 38, 71, 34, 28, 86, 38, 29$ $\newline$ How would the mean change if the number $54$ 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

9

numbers:

\newline

93, 69, 38, 71, 34, 28, 86, 38, 29

\newline

How would the mean change if the number

54

were added to the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Calculate Mean: Step $1$ : List the original set of numbers and calculate the mean. $\newline$ Original set: $93, 69, 38, 71, 34, 28, 86, 38, 29$ . $\newline$ To find the mean, add all the numbers and divide by the total number of numbers. $\newline$ Sum = $93 + 69 + 38 + 71 + 34 + 28 + 86 + 38 + 29 = 486$ . $\newline$ Number of numbers = $9$ . $\newline$ Mean = $486 / 9 = 54$ .
Add Number and Recalculate: Step $2$ : Add the number $54$ to the set and calculate the new mean. $\newline$ New set: $93, 69, 38, 71, 34, 28, 86, 38, 29, 54$ . $\newline$ New sum = $486 + 54 = 540$ . $\newline$ New number of numbers = $10$ . $\newline$ New mean = $540 / 10 = 54$ .
Compare Original and New Mean: Step $3$ : Compare the original mean and the new mean. $\newline$ Original mean = $54$ , New mean = $54$ . $\newline$ Since both means are equal, the mean does not change when $54$ is added.

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