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Sanjay has the following data: $\newline$ $7, 20, 5, c$ $\newline$ If the mode is $5$ , which number could $c$ be? $\newline$ Choices: $\newline$ (A) $5$ $\newline$ (B) $20$

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Write and solve direct variation equations

Full solution

Q. Sanjay has the following data:

\newline

7, 20, 5, c

\newline

If the mode is

5

, which number could

c

be?

\newline

Choices:

\newline

(A)

5

\newline

(B)

20

Identify Mode: Identify the mode of the given data set and understand the definition of mode. Mode is the number that appears most frequently in a data set.
Analyze Data: Analyze the given data: $7$ , $20$ , $5$ , and $c$ . Since the mode is $5$ , $c$ must be a number that makes $5$ appear most frequently.
Check Choices: Check the choices for $c$ : (A) $5$ or (B) $20$ . If $c = 5$ , then the numbers are $7$ , $20$ , $5$ , $5$ . Here, $5$ appears twice, making it the mode. If $c = 20$ , then the numbers are $7$ , $20$ , $5$ , $20$ . Here, $5$ and $20$ both appear twice, so there would be two modes, which contradicts the information that the mode is $5$ .
Conclude Solution: Conclude that $c$ must be $5$ to ensure that $5$ is the only mode of the data set.

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