Find the median of the data 56, 67, 54, 34, 78, 43, 23.

Answer

To find the median of the given data set: 56, 67, 54, 34, 78, 43, 23, we will follow these steps:

### Step 1: Count the Number of Observations
First, we need to count how many numbers are in the data set.

**Data Set:** 56, 67, 54, 34, 78, 43, 23

- Count: 1, 2, 3, 4, 5, 6, 7 (Total = 7 observations)

### Step 2: Arrange the Data in Ascending Order
Next, we will arrange the data in ascending order (from smallest to largest).

**Ascending Order:**
- The smallest value is 23.
- Next is 34.
- Then 43.
- Followed by 54.
- Next is 56.
- Then 67.
- Finally, the largest is 78.

So, the arranged data is: 23, 34, 43, 54, 56, 67, 78.

### Step 3: Determine if the Number of Observations is Odd or Even
Since we have 7 observations (which is odd), we will use the formula for finding the median for an odd number of observations.

### Step 4: Use the Median Formula
The formula for finding the median when the number of observations (n) is odd is:
\[ \text{Median} = \frac{n + 1}{2} \]

Here, \( n = 7 \):
\[ \text{Median Position} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \]

### Step 5: Find the 4th Observation
Now, we will find the 4th observation in our arranged data set.

**Arranged Data:** 23, 34, 43, 54, 56, 67, 78

- The 4th observation is 54.

### Conclusion
Thus, the median of the given data set is **54**.

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