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Look at this set of $10$ numbers: $\newline$ $64, 55, 34, 63, 98, 33, 45, 77, 92, 22$ $\newline$ How would the range change if the number $66$ replaced the number $22$ 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

64, 55, 34, 63, 98, 33, 45, 77, 92, 22

\newline

How would the range change if the number

66

replaced the number

22

in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify original set: Step $1$ : Identify the original set of numbers and calculate the original range. $\newline$ Original set: $64, 55, 34, 63, 98, 33, 45, 77, 92, 22$ $\newline$ Maximum number: $98$ $\newline$ Minimum number: $22$ $\newline$ Original range calculation: $98 - 22 = 76$
Replace with $66$ : Step $2$ : Replace the number $22$ with $66$ in the set and calculate the new range. $\newline$ New set: $64, 55, 34, 63, 98, 33, 45, 77, 92, 66$ $\newline$ Maximum number: $98$ $\newline$ Minimum number: $33$ $\newline$ New range calculation: $98 - 33 = 65$
Compare original vs new range: Step $3$ : Compare the original range with the new range to determine the change. $\newline$ Original range: $76$ $\newline$ New range: $65$ $\newline$ Since $65$ is less than $76$ , the range decreases.

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