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Look at this set of $7$ numbers: $\newline$ $3, 1, 8, 3, 6, 6, 5$ $\newline$ How would the range change if the number $9$ replaced one of the $3$ '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

7

numbers:

\newline

3, 1, 8, 3, 6, 6, 5

\newline

How would the range change if the number

9

replaced one of the

3

'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 $3, 1, 8, 3, 6, 6, 5$ . $\newline$ Arrange the numbers in ascending order: $1, 3, 3, 5, 6, 6, 8$ . $\newline$ Calculate the range: $8 - 1 = 7$ .
Replace and Calculate New Range: Step $2$ : Replace one of the $3$ 's with a $9$ and determine the new range. $\newline$ New set: $1, 3, 5, 6, 6, 8, 9$ . $\newline$ Calculate the new range: $9 - 1 = 8$ .
Compare Original and New Range: Step $3$ : Compare the original range with the new range. $\newline$ Original range: $7$ , New range: $8$ . $\newline$ Since $8$ is greater than $7$ , the range increases.

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