In 10 numbers, arranged in increasing order, the `7^(th)` number is increased by 8, how much will the median be changed ?

Answer

To solve the problem, we need to determine how the median of a set of 10 numbers changes when the 7th number is increased by 8. Let's break this down step by step.

### Step 1: Understand the concept of median
The median is the middle value of a data set. For an even number of observations, the median is calculated as the average of the two middle numbers.

### Step 2: Identify the position of the median
In this case, we have 10 numbers arranged in increasing order. The positions of the numbers are as follows:
- 1st number
- 2nd number
- 3rd number
- 4th number
- 5th number
- 6th number
- 7th number
- 8th number
- 9th number
- 10th number

Since there are 10 numbers (an even count), the median will be the average of the 5th and 6th numbers.

### Step 3: Calculate the initial median
The initial median can be calculated as:
\[ \text{Median} = \frac{\text{5th number} + \text{6th number}}{2} \]

### Step 4: Analyze the effect of increasing the 7th number
When the 7th number is increased by 8, it does not affect the values of the 5th and 6th numbers. The 5th and 6th numbers remain unchanged because they are positioned before the 7th number in the ordered list.

### Step 5: Calculate the new median
Since the 5th and 6th numbers are unchanged, the new median will still be:
\[ \text{New Median} = \frac{\text{5th number} + \text{6th number}}{2} \]

### Step 6: Determine the change in the median
Since the median before and after increasing the 7th number is the same, we conclude that:
\[ \text{Change in Median} = \text{New Median} - \text{Initial Median} = 0 \]

### Final Answer
The median does not change when the 7th number is increased by 8. Therefore, the change in the median is **0**.

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