The points scored by 12 persons are as follows 6, 17,8,9,16, 10, 15, 21, 9, 11, 12 and 16. Find the median.

Options

A. `11.5`
B. `10.4`
C. `11.6`
D. 12

Answer

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

### Step 1: Arrange the scores in ascending order.
The scores given are: 6, 17, 8, 9, 16, 10, 15, 21, 9, 11, 12, and 16.

**Arranging them in ascending order:**
6, 8, 9, 9, 10, 11, 12, 15, 16, 16, 17, 21

### Step 2: Determine the number of data points (n).
We have a total of 12 scores.

**n = 12**

### Step 3: Check if n is even or odd.
Since n = 12, which is even, we will use the formula for finding the median in an even set of numbers.

### Step 4: Use the median formula for even n.
The median is calculated as the average of the two middle numbers. For an even number of observations, the median is given by:

\[ \text{Median} = \frac{\text{(n/2)th term} + \text{((n/2) + 1)th term}}{2} \]

Here, n/2 = 12/2 = 6, so we need to find the 6th and 7th terms.

### Step 5: Identify the 6th and 7th terms in the ordered list.
From our ordered list:
1. 6 (1st)
2. 8 (2nd)
3. 9 (3rd)
4. 9 (4th)
5. 10 (5th)
6. 11 (6th)
7. 12 (7th)

The 6th term is 11 and the 7th term is 12.

### Step 6: Calculate the median.
Now we can calculate the median:

\[ \text{Median} = \frac{11 + 12}{2} = \frac{23}{2} = 11.5 \]

### Final Answer:
The median of the scores is **11.5**.

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