What is the median of distribution: 34, 22, 13, 11, 27, 19, 25, 16?

Options

A. 20.5
B. 21.5
C. 19
D. 22

Answer

To find the median of the given distribution: 34, 22, 13, 11, 27, 19, 25, 16, we will follow these steps:

### Step 1: Arrange the data in ascending order.
We start by sorting the numbers from smallest to largest.

**Sorted Data:** 11, 13, 16, 19, 22, 25, 27, 34

### Step 2: Count the number of terms (n).
Next, we count how many numbers are in our sorted list.

**Count:** There are 8 numbers in total.

### Step 3: Determine if n is even or odd.
Since we have 8 numbers, which is even, we will use the formula for finding the median in an even set of data.

### Step 4: Use the median formula for an even number of terms.
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 = 8, so:
- n/2 = 4
- (n/2) + 1 = 5

### Step 5: Identify the 4th and 5th terms in the sorted data.
From our sorted data:
- 4th term = 19
- 5th term = 22

### Step 6: Calculate the median.
Now we substitute the 4th and 5th terms into the median formula:
\[ \text{Median} = \frac{19 + 22}{2} = \frac{41}{2} = 20.5 \]

### Final Answer:
The median of the distribution is **20.5**.

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