To solve the question, we need to find the average value of the median of the first set of numbers and the mode of the second set of numbers. Let's break it down step by step.
### Step 1: Find the Median of the First Set of Numbers
The first set of numbers is: 2, 8, 3, 7, 4, 6, 7.
1. **Arrange the numbers in ascending order**:
- The ordered set is: 2, 3, 4, 6, 7, 7, 8.
2. **Count the total number of terms**:
- There are 7 terms in total.
3. **Determine if the count is odd or even**:
- Since 7 is odd, the median is the middle number.
4. **Find the position of the median**:
- The position is calculated as (n + 1) / 2 = (7 + 1) / 2 = 4.
- The 4th term in the ordered list is 6.
**Median = 6**
### Step 2: Find the Mode of the Second Set of Numbers
The second set of numbers is: 2, 9, 3, 4, 9, 6, 9.
1. **Arrange the numbers in ascending order**:
- The ordered set is: 2, 3, 4, 6, 9, 9, 9.
2. **Identify the number that appears most frequently**:
- The number 9 appears 3 times, which is more than any other number.
**Mode = 9**
### Step 3: Calculate the Average of the Median and Mode
Now that we have both the median and mode, we can calculate the average.
1. **Use the formula for average**:
- Average = (Median + Mode) / 2
- Average = (6 + 9) / 2
- Average = 15 / 2
- Average = 7.5
### Final Answer
The average value of the median of the first set and the mode of the second set is **7.5**.
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