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Look at this set of $8$ numbers: $\newline$ $7, 6, 4, 2, 6, 8, 1, 2$ $\newline$ 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

7, 6, 4, 2, 6, 8, 1, 2

\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 sets: Step $1$ : Identify the original set and the modified set. $\newline$ Original set: $7, 6, 4, 2, 6, 8, 1, 2$ $\newline$ Modified set: $7, 6, 4, 2, 6, 8, 8, 2$ (replacing $1$ with $8$ )
Calculate ranges: Step $2$ : Calculate the range for both sets. $\newline$ Original range: $\text{Max}(7, 6, 4, 2, 6, 8, 1, 2) - \text{Min}(7, 6, 4, 2, 6, 8, 1, 2) = 8 - 1 = 7$ $\newline$ Modified range: $\text{Max}(7, 6, 4, 2, 6, 8, 8, 2) - \text{Min}(7, 6, 4, 2, 6, 8, 8, 2) = 8 - 2 = 6$
Compare for change: Step $3$ : Compare the ranges to determine the change. $\newline$ Original range: $7$ $\newline$ Modified range: $6$ $\newline$ Since the modified range is less than the original range, the range decreases.

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