What is the median of the following distribution?
67,31, 53, 22, 66, 98, 43, 54, 77, 13, 43, 97, 36, 12, 90, 53

Options

A. 53
B. `56.5`
C. 54
D. `54.5`

Answer

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

### Step 1: List the Numbers
First, we need to list the numbers provided in the question:
67, 31, 53, 22, 66, 98, 43, 54, 77, 13, 43, 97, 36, 12, 90, 53

### Step 2: Count the Total Numbers
Next, we will count how many numbers there are in total. In this case, we have 16 numbers.

### Step 3: Arrange the Numbers in Ascending Order
Now, we will arrange these numbers in ascending order:
12, 13, 22, 31, 36, 43, 43, 53, 53, 54, 66, 67, 77, 90, 97, 98

### Step 4: Identify the Middle Terms
Since there are 16 numbers (an even number), the median will be the average of the two middle terms. The middle terms are the 8th and 9th terms in the ordered list.

### Step 5: Locate the 8th and 9th Terms
From our ordered list:
- The 8th term is 53
- The 9th term is also 53

### Step 6: Calculate the Median
To find the median, we will take the average of the 8th and 9th terms:
\[ \text{Median} = \frac{(8th \text{ term} + 9th \text{ term})}{2} = \frac{(53 + 53)}{2} = \frac{106}{2} = 53 \]

### Final Answer
Thus, the median of the given distribution is **53**.

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