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 step by step, we will analyze how the median is calculated and how it is affected by changing one of the numbers in the sequence.

### Step 1: Understand the Median Calculation
In a set of numbers, the median is the middle value. If the number of observations (n) is even, the median is calculated as the average of the two middle numbers.

**Hint:** Remember that for an even number of observations, the median is the average of the n/2-th and (n/2 + 1)-th terms.

### Step 2: Identify the Number of Observations
In this case, we have 10 numbers, which is an even number.

**Hint:** Identify whether the number of observations is odd or even to determine how to calculate the median.

### Step 3: Calculate the Median
For 10 numbers, the median is calculated as follows:
- The 5th term (T5) and the 6th term (T6) are the two middle numbers.
- The median (M) is given by the formula:
\[ M = \frac{T5 + T6}{2} \]

**Hint:** Write down the formula for the median when the number of terms is even.

### Step 4: Analyze the Effect of Increasing the 7th Number
The problem states that the 7th number (T7) is increased by 8. However, the median depends only on the 5th and 6th terms.

**Hint:** Consider which terms affect the median and which do not when a number in the sequence is changed.

### Step 5: Conclude the Change in Median
Since the 5th and 6th terms are not affected by the change in the 7th term, the median remains unchanged.

**Hint:** Reflect on how changes to numbers outside the middle two terms affect the overall median.

### Final Conclusion
Thus, the median does not change when the 7th number is increased by 8.

**Final Answer:** The median remains the same; there is no change in the median.