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Mia has the following data: $\newline$ $3, 3, 13, a$ $\newline$ If the range is $10$ , which number could $a$ be? $\newline$ Choices: $\newline$ $(A)$ $13$ $\newline$ $(B)$ $1$

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

Full solution

Q. Mia has the following data:

\newline

3, 3, 13, a

\newline

If the range is

10

, which number could

a

be?

\newline

Choices:

\newline

(A)

13

\newline

(B)

1

Understand Range Concept: Understand the concept of range. Range is the difference between the maximum and minimum values in a dataset.
Calculate Current Values: Calculate the current maximum and minimum values without $a$ . $\newline$ Current values: $3$ , $3$ , $13$ $\newline$ Maximum = $13$ , Minimum = $3$
Set Up Equation for Range: Set up the equation for the range with $a$ included. $\text{Range} = \text{Maximum value} - \text{Minimum value} = 10$
Consider 'a' as Maximum: Consider 'a' as the maximum value. $\newline$ If 'a' is maximum, then $a - 3 = 10$ $\newline$ $a = 13 + 10$ $\newline$ $a = 23$

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