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Tommy has the following data: $\newline$ $16, 18, 15, u$ $\newline$ If the mode is $18$ , which number could $u$ be? $\newline$ Choices: $\newline$ (A) $15$ $\newline$ (B) $18$

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

Full solution

Q. Tommy has the following data:

\newline

16, 18, 15, u

\newline

If the mode is

18

, which number could

u

be?

\newline

Choices:

\newline

(A)

15

\newline

(B)

18

Identify Data and Question: Step $1$ : Identify the given data and the question prompt. $\newline$ Tommy has the numbers $16$ , $18$ , $15$ , and an unknown number $u$ . We need to find the value of $u$ such that $18$ is the mode of the dataset.
Definition of Mode: Step $2$ : Understand the definition of mode. $\newline$ The mode is the number that appears most frequently in a dataset. Since $18$ is given as the mode, it must appear more frequently than any other number in the list.
Analyze Choices for $u$ : Step $3$ : Analyze the choices for $u$ . Choices for $u$ are $15$ and $18$ . If $u$ is $15$ , then the numbers are $16$ , $18$ , $15$ , $15$ . If $u$ is $18$ , then the numbers are $16$ , $18$ , $15$ , $18$ .
Determine Mode Choice: Step $4$ : Determine which choice for $u$ makes $18$ the mode. $\newline$ If $u = 15$ , then $15$ and $18$ both appear twice, so there is no single mode. If $u = 18$ , then $18$ appears three times, making it the mode.

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