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Look at this set of $5$ numbers: $\newline$ $68, 96, 86, 68, 81$ $\newline$ How would the range change if the number $59$ were added to 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

5

numbers:

\newline

68, 96, 86, 68, 81

\newline

How would the range change if the number

59

were added to the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify Range: Step $1$ : Identify the current range of the set $68$ , $96$ , $86$ , $68$ , $81$ . $\newline$ To find the range, subtract the smallest number from the largest number in the set. $\newline$ Current smallest number: $68$ $\newline$ Current largest number: $96$ $\newline$ Range = $96 - 68 = 28$
Add Number and Range: Step $2$ : Add the number $59$ to the set and identify the new range. $\newline$ New set: $68, 96, 86, 68, 81, 59$ $\newline$ New smallest number: $59$ (since $59$ is less than $68$ ) $\newline$ New largest number remains $96$ . $\newline$ New Range = $96 - 59 = 37$
Compare Old and New Range: Step $3$ : Compare the old range ( $28$ ) with the new range ( $37$ ). $\newline$ Since $37$ is greater than $28$ , the range has increased.

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