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Look at this set of $6$ numbers: $\newline$ $8, 9, 6, 3, 6, 4$ $\newline$ How would the range change if the number $1$ replaced one of the $6$ '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

6

numbers:

\newline

8, 9, 6, 3, 6, 4

\newline

How would the range change if the number

1

replaced one of the

6

'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 $8, 9, 6, 3, 6, 4$ . $\newline$ To find the range, subtract the smallest number from the largest number in the set. $\newline$ Original smallest number: $3$ , Original largest number: $9$ . $\newline$ Range = $9 - 3 = 6$
Replace with $1$ : Step $2$ : Replace one of the $6$ s with $1$ and find the new range of the set $8, 9, 1, 3, 6, 4$ . $\newline$ New smallest number: $1$ , New largest number remains $9$ . $\newline$ New Range $= 9 - 1 = 8$
Compare ranges: Step $3$ : Compare the original range with the new range. $\newline$ Original Range = $6$ , New Range = $8$ . $\newline$ Since $8$ is greater than $6$ , the range increases

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