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Charlie has the following data: $\newline$ $18, 15, 19, z, 20, 15$ $\newline$ If the range is $5$ , which number could $z$ be? $\newline$ Choices: $\newline$ $(A)$ $18$ $\newline$ $(B)$ $13$

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

Full solution

Q. Charlie has the following data:

\newline

18, 15, 19, z, 20, 15

\newline

If the range is

5

, which number could

z

be?

\newline

Choices:

\newline

(A)

18

\newline

(B)

13

Arrange Data Ascending: Arrange the given data excluding $z$ in ascending order: $15, 15, 18, 19, 20$ . Calculate the current range without $z$ : $20 - 15 = 5$ .
Calculate Current Range: Since the range with $z$ included must also be $5$ , $z$ must be a value that does not increase or decrease the current range. $\newline$ Check if $z = 18$ fits: The range remains $20 - 15 = 5$ .
Check $z = 18$ : Check if $z = 13$ fits: The new range would be $20 - 13 = 7$ , which is not equal to $5$ .

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