To find the median of the data set 4, 5, 9, 2, 6, 8, 7, we will follow these steps:
### Step 1: Arrange the Data in Ascending Order
First, we need to sort the numbers in ascending order. The given data is:
4, 5, 9, 2, 6, 8, 7
When we arrange these numbers in ascending order, we get:
2, 4, 5, 6, 7, 8, 9
### Step 2: Count the Number of Observations
Next, we count how many numbers are in the data set.
The sorted data set is:
2, 4, 5, 6, 7, 8, 9
There are a total of 7 observations.
### Step 3: Determine if the Number of Observations is Odd or Even
Since we have 7 observations, which is an odd number, we will use the formula for finding the median for an odd set of numbers.
### Step 4: Calculate the Position of the Median
To find the median position, we use the formula:
\[
\text{Median Position} = \frac{n + 1}{2}
\]
where \( n \) is the number of observations. Here, \( n = 7 \).
\[
\text{Median Position} = \frac{7 + 1}{2} = \frac{8}{2} = 4
\]
This means the median is the 4th term in the sorted list.
### Step 5: Identify the Median
Now, we look at the sorted data:
2, 4, 5, 6, 7, 8, 9
The 4th term is 6.
### Conclusion
Thus, the median of the data set 4, 5, 9, 2, 6, 8, 7 is **6**.
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