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Katy has the following data: $\newline$ $7, 10, 13, y, 10, 10$ $\newline$ If the mean is $10$ , which number could $y$ be? $\newline$ Choices: $\newline$ (A) $10$ $\newline$ (B) $4$

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

Full solution

Q. Katy has the following data:

\newline

7, 10, 13, y, 10, 10

\newline

If the mean is

10

, which number could

y

be?

\newline

Choices:

\newline

(A)

10

\newline

(B)

4

Calculate Sum and Total: Calculate the sum of the given numbers excluding $y$ and the total number of numbers. $\newline$ Sum excluding $y = 7 + 10 + 13 + 10 + 10 = 50$ . $\newline$ Total numbers = $6$ .
Set Up Mean Equation: Set up the equation for the mean and solve for $y$ . $\text{Mean} = 10$ . $10 = \frac{50 + y}{6}$ . $60 = 50 + y$ .
Solve for y: Solve for y. $\newline$ $y = 60 - 50$ . $\newline$ $y = 10$ .

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