To find the median of the given data set, we will follow these steps:
### Step 1: Combine the Data
First, we need to combine all the numbers from the three groups provided:
- Group 1: 14, 20, 8, 17, 25, 27
- Group 2: 20, 16, 25, 0, 5, 19
- Group 3: 17, 30, 6
Combining these gives us:
14, 20, 8, 17, 25, 27, 20, 16, 25, 0, 5, 19, 17, 30, 6
### Step 2: Sort the Data
Next, we will sort the combined data in increasing order:
0, 5, 6, 8, 14, 16, 17, 17, 19, 20, 20, 25, 25, 27, 30
### Step 3: Count the Total Number of Elements
Now, we count the total number of elements in the sorted data. There are 15 elements in total.
### Step 4: Determine if N is Odd or Even
Since the total number of elements (N) is 15, which is odd, we will use the formula for finding the median in an odd set:
- Median = (N/2 + 1)th element
### Step 5: Calculate the Position of the Median
Now, we calculate the position of the median:
N/2 = 15/2 = 7.5
We take the integer part, which is 7, and add 1:
7 + 1 = 8
### Step 6: Find the 8th Element
Now we find the 8th element in the sorted list:
1. 0
2. 5
3. 6
4. 8
5. 14
6. 16
7. 17
8. 17
The 8th element is 17.
### Step 7: Conclusion
Thus, the median of the given data set is **17**.
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