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Look at this set of $8$ numbers: $\newline$ $32, 36, 47, 78, 26, 41, 27, 32$ $\newline$ How would the range change if the number $87$ replaced one of the $32$ 's 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

32, 36, 47, 78, 26, 41, 27, 32

\newline

How would the range change if the number

87

replaced one of the

32

's in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify original range: Step $1$ : Identify the original range of the set. $\newline$ Original set: $32, 36, 47, 78, 26, 41, 27, 32$ . $\newline$ Arrange in ascending order: $26, 27, 32, 32, 36, 41, 47, 78$ . $\newline$ Calculate the range: $78 - 26 = 52$ .
Replace with $87$ : Step $2$ : Replace one of the $32$ 's with $87$ and find the new range. $\newline$ New set: $26, 27, 32, 36, 41, 47, 78, 87$ . $\newline$ Arrange in ascending order: $26, 27, 32, 36, 41, 47, 78, 87$ . $\newline$ Calculate the new range: $87 - 26 = 61$ .
Compare ranges: Step $3$ : Compare the original range with the new range. $\newline$ Original range: $52$ , New range: $61$ . $\newline$ Since $61$ is greater than $52$ , the range increases.

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