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Look at this set of $6$ numbers: $\newline$ $3, 6, 3, 3, 9, 5$ $\newline$ How would the mode change if the number $6$ 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

6

numbers:

\newline

3, 6, 3, 3, 9, 5

\newline

How would the mode change if the number

6

were added to the set?

\newline

Choices:

\newline

(A) increase

\newline

(B) decrease

\newline

(C) no change

Identify Mode: Identify the mode of the original set. $\newline$ The original set is $3, 6, 3, 3, 9, 5$ . The number $3$ appears most frequently ( $3$ times). $\newline$ Mode of original set: $3$
Add Number and Identify Mode: Add the number $6$ to the set and identify the new mode. $\newline$ New set: $3, 6, 3, 3, 9, 5, 6$ . Now, the number $3$ still appears most frequently ( $3$ times), and the number $6$ appears twice. $\newline$ Mode of new set: $3$
Compare Original and New Mode: Compare the mode of the original set and the new set. $\newline$ The mode remains $3$ in both sets, so adding another $6$ does not change the mode.

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