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Look at this set of $8$ numbers: $\newline$ $89, 58, 78, 58, 58, 42, 12, 98$ $\newline$ How would the range change if the number $71$ replaced the number $12$ 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

89, 58, 78, 58, 58, 42, 12, 98

\newline

How would the range change if the number

71

replaced the number

12

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify Range: Identify the original range of the set: $\newline$ Numbers: $89, 58, 78, 58, 58, 42, 12, 98$ $\newline$ Maximum number: $98$ $\newline$ Minimum number: $12$ $\newline$ Original range calculation: $98 - 12 = 86$
Replace Number and Calculate: Replace the number $12$ with $71$ and find the new range: $\newline$ New set of numbers: $89$ , $58$ , $78$ , $58$ , $58$ , $42$ , $71$ , $98$ $\newline$ New maximum number: $98$ $\newline$ New minimum number: $42$ $\newline$ New range calculation: $71$ $2$
Compare Original and New Range: Compare the original range with the new range: $\newline$ Original range: $86$ $\newline$ New range: $56$ $\newline$ Since $56$ is less than $86$ , the range decreases.

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