The problem states that the given dataset is missing a number. We are given the range of the dataset as 25.5. We need to find two possible values of the missing number. The given data set is $9, 0, -2, 4.5, 8, 7.5, -1.5, 13.5, 19, -1, 2$.

1. Problem Description

The problem states that the given dataset is missing a number. We are given the range of the dataset as 25.

5. We need to find two possible values of the missing number.

The given data set is $9, 0, -2, 4.5, 8, 7.5, -1.5, 13.5, 19, -1, 2$.

2. Solution Steps

First, let's sort the given data set in ascending order:

$-2, -1.5, -1, 0, 2, 4.5, 7.5, 8, 9, 13.5, 19$

The range of a dataset is the difference between the largest and smallest values.

Range = Largest Value - Smallest Value

The current largest value is 19 and the smallest is -

2. So the current range is $19 - (-2) = 21$. Since the actual range is 25.5, we need to either decrease the smallest value or increase the largest value.

Case 1: We increase the largest value. Let the missing number be $x$. If $x$ is the new largest number, then the range becomes $x - (-2) = 25.5$.

$x + 2 = 25.5$

$x = 25.5 - 2$

$x = 23.5$

Case 2: We decrease the smallest value. Let the missing number be $y$. If $y$ is the new smallest number, then the range becomes $19 - y = 25.5$.

$-y = 25.5 - 19$

$-y = 6.5$

$y = -6.5$

Therefore, the two possible missing numbers are 23.5 and -6.

5.

3. Final Answer

The two possible missing numbers are 23.5 and -6.

5.