The median for the given set of six ordered data values is 31.5 . $$ 51225 \_4148 $$ What is the missing value? The missing value is

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To determine the missing value in the ordered data set, let's break down the information provided:

1. **Ordered Data Set**: The given data appears as `5, 12, 25, _, 41, 48`. Here, the underscore `_` represents the missing value, which we'll denote as $$ x $$.

2. **Number of Data Points**: There are six data points in total.

3. **Median of the Data Set**: For an even number of data points, the median is the average of the third and fourth values. It's given that the median is 31.5.

$$
   \text{Median} = \frac{\text{3rd value} + \text{4th value}}{2} = 31.5
   $$

4. **Setting Up the Equation**:

$$
   \frac{25 + x}{2} = 31.5
   $$

5. **Solving for $$ x $$**:

$$
   25 + x = 63 \quad (\text{Multiplying both sides by 2})
   $$
   $$
   x = 63 - 25
   $$
   $$
   x = 38
   $$

6. **Verification**: The missing value $$ x = 38 $$ fits correctly within the ordered sequence between 25 and 41.

**Therefore, the missing value is 38.**

Answer: 38
The missing value is 38.

The median for the given set of six ordered data values is 31.5 . \( 51225 \_4148 \) What is the missing value? The missing value is

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