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Look at this set of $8$ numbers: $\newline$ $9, 2, 8, 1, 3, 2, 7, 5$ $\newline$ How would the mode change if the number $9$ replaced one of the $2$ 's in the set? $\newline$ Choices: $\newline$ (A)increase $\newline$ (B)decrease $\newline$ (C)no change $\newline$

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Changes in mean, median, mode, and range

Full solution

Q. Look at this set of

8

numbers:

\newline

9, 2, 8, 1, 3, 2, 7, 5

\newline

How would the mode change if the number

9

replaced one of the

2

's in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

\newline

Identify Mode of Original Set: Identify the mode of the original set. $\newline$ Original set: $9, 2, 8, 1, 3, 2, 7, 5$ $\newline$ The number $2$ appears twice, which is more frequent than any other number. $\newline$ Mode of original set: $2$
Replace Number with $9$ : Replace one of the $2$ 's with a $9$ . $\newline$ New set: $9, 9, 8, 1, 3, 2, 7, 5$ $\newline$ Now, the number $9$ appears twice, matching the frequency of the remaining $2$ .
Identify Mode of New Set: Identify the mode of the new set. $\newline$ In the new set, both $9$ and $2$ appear twice. There are two modes now: $9$ and $2$ .
Compare Original and New Modes: Compare the mode of the original set to the new set. $\newline$ Original mode: $2$ $\newline$ New modes: $9$ and $2$ $\newline$ The mode has increased by including an additional number ( $9$ ) as a mode.

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