\text{Assertion (A): If the median of the given data (provided in ascending order):}26,29,42,53,x,x+2,70,75,82,93\text{, is 60 then the value of}x\text{is 59.}

\text{Reason (R): When the number of observations (}n\text{) is even, the median is the value of}\frac{1}{2}\left(\text{sum of middle terms}\right)\text{provided data is arranged in accending order.}

The correct option is: Both Assertion (A) and Reason are true and R is the correct explanation of A.

Let us analyze both the Assertion (A) and the Reason (R) step-by-step to understand why this option is correct.

Step 1: Analyze the Reason (R)
The Reason states that when the number of observations, $n$, is even, the median of the data (arranged in ascending order) is the average (or $\frac{1}{2}$ times the sum) of the middle two terms.
Specifically, for an even number of observations $n$, the middle terms are the ${\left(\frac{n}{2}\right)}^{\text{th}}$ observation and the ${(\frac{n}{2}+1)}^{\text{th}}$ observation.
The formula for the median is indeed:

$$\text{Median}=\frac{1}{2}[{\left(\frac{n}{2}\right)}^{\text{th}}\text{observation}+{(\frac{n}{2}+1)}^{\text{th}}\text{observation}]$$

Since this formula correctly defines the median for an even number of sorted observations, Reason (R) is true.

Step 2: Analyze the Assertion (A)
The given data set arranged in ascending order is:
26, 29, 42, 53, x, x + 2, 70, 75, 82, 93
Let us count the number of observations (n):
Here, $n=10$, which is an even number.
Since n is even, we use the method defined in Reason (R) to find the median. The two middle terms are:
- The ${\left(\frac{10}{2}\right)}^{\text{th}}$ term, which is the 5th term = $x$
- The ${(\frac{10}{2}+1)}^{\text{th}}$ term, which is the 6th term = $x+2$

Using the median formula:

$$\text{Median}=\frac{\text{5th term}+\text{6th term}}{2}$$

Given that the median is 60, we can substitute the values into the equation:

$$60=\frac{x+(x+2)}{2}$$

Multiply both sides by 2 to clear the fraction:

$$120=2x+2$$

Subtract 2 from both sides:

$$2x=118$$

Divide by 2:

$$x=59$$

Since solving for $x$ gives 59, Assertion (A) is true.

Conclusion
Both Assertion (A) and Reason (R) are true. Furthermore, the Reason (R) provides the exact mathematical framework (formula for the median of an even number of terms) used to calculate the value of $x$ and verify the Assertion (A). Therefore, Reason (R) is the correct explanation of Assertion (A).