https://file.aiquickdraw.com/mathbot/file/1726622592922irolgaev.jpg

Given the problem, the ordered set of six values is: \(9, 12, 25, \text{?}, 41, 51\). The median of this set is provided as 32.5. We need to find the missing value.

### **Step-by-step Solution:**
1. Since there are six numbers, the median will be the average of the 3rd and 4th numbers when arranged in ascending order.
2. Currently, the 3rd number is 25, and the 4th number is the missing value (let's call it \(x\)).
3. According to the definition of the median: 
   \[
   \text{Median} = \frac{25 + x}{2} = 32.5
   \]
4. To solve for \(x\), multiply both sides by 2:
   \[
   25 + x = 65
   \]
5. Subtract 25 from both sides:
   \[
   x = 40
   \]

### **Conclusion:**
The missing value is **40**.

Would you like more details or have any questions? 

Here are 5 related questions to explore this concept further:
1. How do you find the median of a set with an odd number of elements?
2. What happens to the median if you change one of the values in the set?
3. How would you find the mean of this data set?
4. Can the median be one of the data values in all cases?
5. What is the effect of outliers on the median of a data set?

**Tip:** The median is a good measure of central tendency for data sets with outliers, as it is not as affected by extremely high or low values as the mean.

The median for the given set of six ordered data values is 32.5. The numbers are: 9, 12, 25, ?, 41, 51. What is the missing value?

This problem explores how to find a missing value in a set of six ordered numbers when the median is known. The set includes 9, 12, 25, ?, 41, 51 with a median of 32.5. Learn how to use the median formula to solve this question.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation