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Simon has the following data: $\newline$ $6, 10, b, 18, 9$ $\newline$ If the range is $16$ , which number could $b$ be? $\newline$ Choices: $\newline$ (A) $2$ $\newline$ (B) $15$

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

Full solution

Q. Simon has the following data:

\newline

6, 10, b, 18, 9

\newline

If the range is

16

, which number could

b

be?

\newline

Choices:

\newline

(A)

2

\newline

(B)

15

Understand Problem: Step $1$ : Understand the problem and identify the known values. $\newline$ Simon has the data set: $6, 10, b, 18, 9$ . The range of the data set is given as $16$ . The range is the difference between the maximum and minimum values in the data set.
Calculate Possible Values: Step $2$ : Calculate the possible values for $b$ using the range. $\newline$ The range is the maximum value minus the minimum value, which equals $16$ . We need to find $b$ such that the range remains $16$ when $b$ is either the maximum or minimum value. $\newline$ If $b$ is the maximum value: $\newline$ $b - \min(6, 10, 9) = 16$ $\newline$ $b - 6 = 16$ $\newline$ $b = 22$ (This value is not in the choices, so $b$ cannot be the maximum value.) $\newline$ If $b$ is the minimum value: $\newline$ $16$ $1$ $\newline$ $16$ $2$ $\newline$ $16$ $3$
Check Calculated Value: Step $3$ : Check if the calculated value of $b$ is among the choices. $\newline$ From the calculation, $b = 2$ is a possible value and it is listed in the choices as option (A).

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