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

Understand Problem: Step 1: Understand the problem and identify the known values. 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. 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. If b is the maximum value: b - min(6, 10, 9) = 16 b - 6 = 16 b = 22 (This value is not in the choices, so b cannot be the maximum value.) If b is the minimum value: max(6, 10, 18, 9) - b = 16 18 - b = 16 b = 2 Check Calculated Value: Step 3: Check if the calculated value of b is among the choices. From the calculation, b = 2 is a possible value and it is listed in the choices as option (A).

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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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Math Problems

Grade 7

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

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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).