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Look at this set of $9$ numbers: $\newline$ $9, 5, 5, 9, 8, 8, 6, 4, 5$ $\newline$ How would the mode change if the number $9$ replaced one of the $5$ '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

9

numbers:

\newline

9, 5, 5, 9, 8, 8, 6, 4, 5

\newline

How would the mode change if the number

9

replaced one of the

5

's in the set?

\newline

Choices:

\newline

(A)increase

\newline

(B)decrease

\newline

(C)no change

\newline

Identify Mode: Step $1$ : List the original set of numbers and identify the mode. $\newline$ Original set: $9, 5, 5, 9, 8, 8, 6, 4, 5$ . $\newline$ Mode is the number that appears most frequently. Here, ' $5$ ' appears three times, which is more than any other number.
Replace and Count: Step $2$ : Replace one of the ' $5$ 's with a ' $9$ ' and list the new set of numbers. $\newline$ New set: $9, 5, 9, 9, 8, 8, 6, 4, 5$ . $\newline$ Now, count the frequency of each number again. $\newline$ ' $9$ ' appears three times, and ' $5$ ' appears two times.
Determine New Mode: Step $3$ : Determine the new mode after the replacement. $\newline$ In the new set, both ' $9$ ' and ' $5$ ' were candidates for the mode. However, after replacing one ' $5$ ' with ' $9$ ', ' $9$ ' now appears four times, making it the new mode.

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