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Look at this set of $8$ numbers: $\newline$ $62, 47, 83, 50, 52, 54, 82, 90$ $\newline$ How would the mean change if the number $47$ 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

8

numbers:

\newline

62, 47, 83, 50, 52, 54, 82, 90

\newline

How would the mean change if the number

47

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: $62, 47, 83, 50, 52, 54, 82, 90$ . $\newline$ Sum of original set = $62 + 47 + 83 + 50 + 52 + 54 + 82 + 90 = 520$ . $\newline$ Number of elements in original set = $8$ . $\newline$ Original mean = $520 / 8 = 65$ .
Calculate New Mean: Calculate the new mean after adding $47$ to the set. $\newline$ New set: $62, 47, 83, 50, 52, 54, 82, 90, 47$ . $\newline$ Sum of new set = $520 + 47 = 567$ . $\newline$ Number of elements in new set = $9$ . $\newline$ New mean = $567 / 9 = 63$ .
Compare Means: Compare the original mean to the new mean. Original mean = $65$ ; New mean = $63$ . Since $63$ is less than $65$ , the mean decreases.

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