Assertion : The median of 83, 37, 70, 29, 45, 63, 41, 70, 34, 54, is 49.5.
Reason : The median of n odd number of observations is`((n+1)/2)^("th")` term.

Options

A. If both assertion and reason are true and reason is the correct explanation of assertion.
B. If both assertion and reason are true but reason is not tlie correct explanation of assertion.
C. If assertion is true but reason is false.
D. If assertion is false but reason is true.

Answer

To solve the problem, we need to determine whether the assertion and reason provided are true or false.

### Step 1: Identify the data set
The given data set is:
83, 37, 70, 29, 45, 63, 41, 70, 34, 54

### Step 2: Count the number of observations
Count the number of observations in the data set:
- There are 10 observations.

### Step 3: Determine if the number of observations is odd or even
Since 10 is an even number, we will use the formula for the median of an even number of observations.

### Step 4: Arrange the data in ascending order
Arrange the data in ascending order:
- 29, 34, 37, 41, 45, 54, 63, 70, 70, 83

### Step 5: Find the median
For an even number of observations (n = 10), the median is calculated as:
\[ \text{Median} = \frac{\text{(n/2)th term} + \text{(n/2 + 1)th term}}{2} \]
Here, n/2 = 10/2 = 5, so we take the 5th and 6th terms.

- 5th term = 45
- 6th term = 54

Now, calculate the median:
\[ \text{Median} = \frac{45 + 54}{2} = \frac{99}{2} = 49.5 \]

### Conclusion on Assertion
The assertion states that the median is 49.5, which we have calculated to be true.

### Conclusion on Reason
The reason states that the median of n odd number of observations is \(\frac{(n+1)}{2}\)th term. However, since we have an even number of observations (10), the reason is not applicable in this case.

### Final Answer
- Assertion: True
- Reason: False