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Colton has the following data: $\newline$ $19, 14, 16, h, 16$ $\newline$ If the mean is $15$ , which number could $h$ be? $\newline$ Choices: $\newline$ $(A)$ $10$ $\newline$ $(B)$ $25$

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

Full solution

Q. Colton has the following data:

\newline

19, 14, 16, h, 16

\newline

If the mean is

15

, which number could

h

be?

\newline

Choices:

\newline

(A)

10

\newline

(B)

25

Calculate sum excluding h: Calculate the sum of the given numbers excluding $h$ to find the total sum needed for a mean of $15$ . $\newline$ Sum of known numbers = $19 + 14 + 16 + 16 = 65$ $\newline$ Mean formula: $(\text{Total sum of all numbers}) / (\text{Number of numbers}) = \text{Mean}$ $\newline$ Here, $(65 + h) / 5 = 15$
Solve for h: Solve for h. $\newline$ $(65 + h) / 5 = 15$ $\newline$ Multiply both sides by $5$ to isolate the term with $h$ . $\newline$ $65 + h = 75$
Subtract to find $h$ : Subtract $65$ from both sides to solve for $h$ . $\newline$ $h = 75 - 65$ $\newline$ $h = 10$

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