15 observations are arranged in ascending order. 9th observations is increased by 2. Then the new median will.

Options

A. increases by 2
B. Deacreases by 2
C. no change
D. Becomes two times

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Understand the given data
We have 15 observations arranged in ascending order. Since the number of observations (n) is odd, we can use the formula for finding the median.

### Step 2: Calculate the position of the median
For an odd number of observations, the median is located at the position given by the formula:
\[ \text{Median Position} = \frac{n + 1}{2} \]
Here, \( n = 15 \):
\[ \text{Median Position} = \frac{15 + 1}{2} = \frac{16}{2} = 8 \]
Thus, the median is the 8th observation.

### Step 3: Analyze the effect of increasing the 9th observation
According to the problem, the 9th observation is increased by 2. However, we need to determine if this change affects the median.

### Step 4: Determine if the median changes
Since the median is the 8th observation, and the 9th observation is increased, we need to check if the 8th observation is affected. The 8th observation remains unchanged regardless of the change made to the 9th observation.

### Step 5: Conclusion
Since the 8th observation (which is the median) is unaffected by the change made to the 9th observation, the new median will remain the same as the original median.

### Final Answer
The new median will not change.

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