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Look at this set of $7$ numbers: $\newline$ $4, 7, 1, 1, 7, 4, 7$ $\newline$ How would the mode change if the number $7$ 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

7

numbers:

\newline

4, 7, 1, 1, 7, 4, 7

\newline

How would the mode change if the number

7

were added to the set?

\newline

Choices:

\newline

(A) increase

\newline

(B) decrease

\newline

(C) no change

Identify Mode of Original Set: Identify the mode of the original set: $4, 7, 1, 1, 7, 4, 7$ . $\newline$ Count each number: $\newline$ - $1$ appears $2$ times $\newline$ - $4$ appears $2$ times $\newline$ - $7$ appears $3$ times $\newline$ The mode is $7$ , as it appears most frequently.
Add Number to Set: Add the number $7$ to the set, making the new set: $4, 7, 1, 1, 7, 4, 7, 7$ . Count the occurrences of each number in the new set: $\newline$ - $1$ appears $2$ times $\newline$ - $4$ appears $2$ times $\newline$ - $7$ appears $4$ times $\newline$ The mode remains $7$ , but now it appears even more frequently.
Compare Original and New Mode: Compare the mode of the original set and the new set. $\newline$ Original mode: $7$ $\newline$ New mode: $7$ $\newline$ The mode does not change in value, but the frequency of the mode increases.

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