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Look at this set of $8$ numbers: $\newline$ $98, 53, 48, 39, 45, 56, 11, 50$ $\newline$ How would the mean change if the number $83$ replaced the number $11$ 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

98, 53, 48, 39, 45, 56, 11, 50

\newline

How would the mean change if the number

83

replaced the number

11

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: $98, 53, 48, 39, 45, 56, 11, 50$ $\newline$ Sum of original set = $98 + 53 + 48 + 39 + 45 + 56 + 11 + 50 = 400$ $\newline$ Number of elements = $8$ $\newline$ Original mean = $400 / 8 = 50$
Replace and Calculate New Sum: Replace the number $11$ with $83$ and calculate the new sum. $\newline$ New set: $98, 53, 48, 39, 45, 56, 83, 50$ $\newline$ Sum of new set = $98 + 53 + 48 + 39 + 45 + 56 + 83 + 50 = 472$
Calculate New Mean: Calculate the new mean of the set. $\newline$ New mean = $\frac{472}{8} = 59$
Compare Original and New Mean: Compare the original mean with the new mean. $\newline$ Original mean = $50$ , New mean = $59$ $\newline$ Since $59$ is greater than $50$ , the mean increases.

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