Find the median of the following distribution:
40, 49, 17, 68, 44, 62, 48, 47, 21, 55, 32, 50, 12, 27, 30, 18

Answer

To find the median of the given distribution, we will follow these steps:

### Step 1: Arrange the data in ascending order
We start with the given numbers:
40, 49, 17, 68, 44, 62, 48, 47, 21, 55, 32, 50, 12, 27, 30, 18.

Now, we will arrange these numbers in ascending order:
12, 17, 18, 21, 27, 30, 32, 40, 44, 47, 48, 49, 50, 55, 62, 68.

### Step 2: Count the number of observations
Next, we need to count the total number of observations (n). In this case, we have:
1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16.

So, n = 16.

### Step 3: Determine if n is odd or even
Since n = 16, which is an even number, we will use the formula for finding the median in an even distribution.

### Step 4: Use the median formula for even n
The formula for the median when n is even is:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{((n/2) + 1)th term}}{2} \]

Here, n/2 = 16/2 = 8. So, we need to find the 8th and 9th terms in the ordered list.

### Step 5: Identify the 8th and 9th terms
From the ordered list:
1. 12
2. 17
3. 18
4. 21
5. 27
6. 30
7. 32
8. **40** (8th term)
9. **44** (9th term)

### Step 6: Calculate the median
Now, we will calculate the median using the 8th and 9th terms:
\[ \text{Median} = \frac{40 + 44}{2} = \frac{84}{2} = 42. \]

### Final Answer
Thus, the median of the given distribution is **42**.

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