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Addison has the following data: $\newline$ $11, c, 4, 9, 7, 12$ $\newline$ If the mean is $9$ , which number could $c$ be? $\newline$ Choices: $\newline$ $(A)$ $5$ $\newline$ $(B)$ $11$

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

Full solution

Q. Addison has the following data:

\newline

11, c, 4, 9, 7, 12

\newline

If the mean is

9

, which number could

c

be?

\newline

Choices:

\newline

(A)

5

\newline

(B)

11

Calculate total number of terms: Calculate the total number of terms in the data set. $\newline$ Data set: $11, c, 4, 9, 7, 12$ $\newline$ Number of terms: $6$
Set up mean equation: Set up the equation using the mean formula. $\newline$ Mean formula: Mean = $\frac{\text{sum of all terms}}{\text{number of terms}}$ $\newline$ Given mean = $9$ $\newline$ $9 = \frac{11 + c + 4 + 9 + 7 + 12}{6}$
Simplify sum in equation: Simplify the sum inside the equation. $\newline$ Sum of known terms = $11 + 4 + 9 + 7 + 12 = 43$ $\newline$ $9 = (43 + c) / 6$
Solve for c: Solve for c. $\newline$ Multiply both sides by $6$ to clear the fraction: $\newline$ $9 \times 6 = (43 + c)$ $\newline$ $54 = 43 + c$
Isolate c: Isolate c. $\newline$ $54 - 43 = c$ $\newline$ $c = 11$

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