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Look at this set of $8$ numbers: $\newline$ $8, 8, 2, 3, 8, 5, 8, 9$ $\newline$ How would the range change if the number $2$ replaced the number $5$ 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

8, 8, 2, 3, 8, 5, 8, 9

\newline

How would the range change if the number

2

replaced the number

5

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: $8, 8, 2, 3, 8, 5, 8, 9$ . $\newline$ To find the range, subtract the smallest number from the largest number. $\newline$ Range = $9 - 2 = 7$ .
Modify Set: Step $2$ : Modify the set by replacing the number $5$ with the number $2$ . $\newline$ Modified set: $8, 8, 2, 3, 8, 2, 8, 9$ . $\newline$ Now, find the new range. $\newline$ Range = $9 - 2 = 7$ .
Compare Ranges: Step $3$ : Compare the original range with the new range. $\newline$ Original Range = $7$ , New Range = $7$ . $\newline$ Since both ranges are equal, the range does not change.

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