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Look at this set of $8$ numbers: $\newline$ $33, 74, 32, 76, 59, 34, 73, 26$ $\newline$ How would the range change if the number $86$ 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

8

numbers:

\newline

33, 74, 32, 76, 59, 34, 73, 26

\newline

How would the range change if the number

86

were added to the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

Identify current range: Step $1$ : Identify the current range of the set. $\newline$ Current set: $33, 74, 32, 76, 59, 34, 73, 26$ . $\newline$ Arrange in ascending order: $26, 32, 33, 34, 59, 73, 74, 76$ . $\newline$ Current minimum = $26$ , Current maximum = $76$ . $\newline$ Current range = Maximum - Minimum = $76 - 26 = 50$ .
Add new number and find range: Step $2$ : Add the new number to the set and find the new range. $\newline$ New number added: $86$ . $\newline$ New set: $26, 32, 33, 34, 59, 73, 74, 76, 86$ . $\newline$ New minimum still = $26$ , New maximum = $86$ . $\newline$ New range = New maximum - New minimum = $86 - 26 = 60$ .
Compare old and new range: Step $3$ : Compare the old range with the new range. $\newline$ Old range = $50$ , New range = $60$ . $\newline$ Since 60 > 50, the range increases.

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