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Look at this set of $10$ numbers: $\newline$ $9, 7, 7, 4, 4, 2, 6, 7, 7, 7$ $\newline$ How would the range change if the number $3$ replaced the number $9$ 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

10

numbers:

\newline

9, 7, 7, 4, 4, 2, 6, 7, 7, 7

\newline

How would the range change if the number

3

replaced the number

9

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: $9, 7, 7, 4, 4, 2, 6, 7, 7, 7$ $\newline$ Arrange in ascending order: $2, 4, 4, 6, 7, 7, 7, 7, 7, 9$ $\newline$ Original range calculation: $9 - 2 = 7$
Replace Number $9$ : Step $2$ : Replace the number $9$ with $3$ and find the new range. $\newline$ New set: $3, 7, 7, 4, 4, 2, 6, 7, 7, 7$ $\newline$ Arrange in ascending order: $2, 3, 4, 4, 6, 7, 7, 7, 7, 7$ $\newline$ New range calculation: $7 - 2 = 5$
Compare Original and New Range: Step $3$ : Compare the original range with the new range. $\newline$ Original range: $7$ $\newline$ New range: $5$ $\newline$ Since $5$ is less than $7$ , the range has decreased.

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