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Look at this set of $8$ numbers: $\newline$ $9, 8, 9, 1, 2, 3, 8, 9$ $\newline$ How would the range change if the number $8$ replaced the number $1$ 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

9, 8, 9, 1, 2, 3, 8, 9

\newline

How would the range change if the number

8

replaced the number

1

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify Numbers and Change: Step $1$ : Identify the original set of numbers and the proposed change. $\newline$ Original set: $9, 8, 9, 1, 2, 3, 8, 9$ $\newline$ Change: Replace $1$ with $8$
Calculate Original Range: Step $2$ : Calculate the range of the original set. $\newline$ Original set sorted: $1, 2, 3, 8, 8, 9, 9, 9$ $\newline$ Range $= \text{Maximum} - \text{Minimum} = 9 - 1 = 8$
Modify Set and New Range: Step $3$ : Modify the set as proposed and calculate the new range. $\newline$ Modified set: $9, 8, 9, 8, 2, 3, 8, 9$ $\newline$ Modified set sorted: $2, 3, 8, 8, 8, 9, 9, 9$ $\newline$ New Range $= \text{Maximum} - \text{Minimum} = 9 - 2 = 7$
Compare Original and New Range: Step $4$ : Compare the original and new ranges to determine the change. $\newline$ Original Range = $8$ $\newline$ New Range = $7$ $\newline$ Since $7$ is less than $8$ , the range decreases.

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