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Dan has the following data: $\newline$ $14, 15, 14, y, 15, 18$ $\newline$ If the mode is $15$ , which number could $y$ be? $\newline$ Choices: $\newline$ $(A)$ $15$ $\newline$ $(B)$ $14$

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Mean, median, mode, and range: find the missing number

Full solution

Q. Dan has the following data:

\newline

14, 15, 14, y, 15, 18

\newline

If the mode is

15

, which number could

y

be?

\newline

Choices:

\newline

(A)

15

\newline

(B)

14

Understand the problem: Step $1$ : Understand the problem and the data given. $\newline$ Dan has the numbers $14$ , $15$ , $14$ , $y$ , $15$ , $18$ , and we know the mode is $15$ . The mode is the number that appears most frequently in a set of data.
Analyze frequency: Step $2$ : Analyze the frequency of the existing numbers. $\newline$ Currently, the number $15$ appears twice, and the number $14$ also appears twice. The number $18$ appears once.
Determine possible values: Step $3$ : Determine the possible values for $y$ that would keep $15$ as the mode. $\newline$ If $y$ is $15$ , then $15$ would appear three times, making it still the mode. If $y$ is $14$ , then $14$ would appear three times, tying with $15$ for the mode. However, since the problem states that the mode is $15$ , $y$ cannot be $14$ because it would change the mode to both $14$ and $15$ .

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