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Sophia has the following data: $\newline$ $11, 10, 10, 12, u$ $\newline$ If the mean is $11$ , which number could $u$ be? $\newline$ Choices: $\newline$ $(A)$ $12$ $\newline$ $(B)$ $7$

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

Full solution

Q. Sophia has the following data:

\newline

11, 10, 10, 12, u

\newline

If the mean is

11

, which number could

u

be?

\newline

Choices:

\newline

(A)

12

\newline

(B)

7

Calculate Sum: Calculate the sum of the given numbers excluding $u$ . $\newline$ Sum = $11 + 10 + 10 + 12$ $\newline$ Sum = $43$
Find Total Sum: Use the mean formula to find the total sum of all numbers. $\newline$ Mean = $11$ $\newline$ Total numbers = $5$ $\newline$ Total sum = Mean $\times$ Total numbers $\newline$ Total sum = $11 \times 5$ $\newline$ Total sum = $55$
Solve for u: Solve for u by subtracting the sum of the known numbers from the total sum. $\newline$ Total sum = Sum of known numbers + $u$ $\newline$ $55 = 43 + u$ $\newline$ $u = 55 - 43$ $\newline$ $u = 12$

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