Step 1: Organize the data and calculate basic sums

The given data with frequency distribution is: $\begin{array}{ccccccc} x_i & 3 & 8 & 11 & 10 & 5 & 4 \\ f_i & 5 & 2 & 3 & 2 & 4 & 4 \end{array}$ First, let's arrange the data in ascending order of $x_i$ to make calculations for the median and other measures easier.

Now, let's calculate the total number of observations, $N = \sum f_i$. $N = 5 + 4 + 4 + 2 + 2 + 3 = 20$.

Step 2: Calculate the Mean (P)

The formula for the mean ($\bar{x}$) of a frequency distribution is $\bar{x} = \frac{\sum f_i x_i}{\sum f_i}$. Let's calculate $\sum f_i x_i$:

$\sum f_i x_i = 120$.

Mean, $\bar{x} = \frac{120}{20} = 6$.

So, (P) The mean of the above data is 6, which corresponds to (3) in List-II.

Step 3: Calculate the Median (Q)

To find the median, we need the cumulative frequency (c.f.). The total number of observations is $N=20$ (even). The median is the average of the $\frac{N}{2}^{th}$ and $(\frac{N}{2} + 1)^{th}$ observations, i.e., the 10th and 11th observations.

Let's create the cumulative frequency table:

The cumulative frequency just greater than or equal to 10 is 13, which corresponds to $x_i = 5$. This means the 10th observation is 5. Since the 10th, 11th, 12th, and 13th observations are all 5, the 11th observation is also 5.

Median, $M = \frac{10^{th} \text{ observation} + 11^{th} \text{ observation}}{2} = \frac{5 + 5}{2} = 5$.

So, (Q) The median of the above data is 5, which corresponds to (2) in List-II.

Step 4: Calculate the Mean Deviation about the Mean (R)

The formula for the mean deviation about the mean is $MD(\bar{x}) = \frac{\sum f_i |x_i - \bar{x}|}{N}$. We have $\bar{x} = 6$ and $N = 20$.

Let's calculate $\sum f_i |x_i - 6|$:

| $x_i$ | $f_i$ | $|x_i - \bar{x}| = |x_i - 6|$ | $f_i |x_i - \bar{x}|$ | | :---: | :---: | :--------------------------: | :-----------------------: | | 3 | 5 | 3 | $5 \times 3 = 15$ | | 4 | 4 | 2 | $4 \times 2 = 8$ | | 5 | 4 | 1 | $4 \times 1 = 4$ | | 8 | 2 | 2 | $2 \times 2 = 4$ | | 10 | 2 | 4 | $2 \times 4 = 8$ | | 11 | 3 | 5 | $3 \times 5 = 15$ | | Total | 20 | | 54 |

$MD(\bar{x}) = \frac{54}{20} = 2.7$.

So, (R) The mean deviation about the mean is 2.7, which corresponds to (4) in List-II.

Step 5: Calculate the Mean Deviation about the Median (S)

The formula for the mean deviation about the median is $MD(M) = \frac{\sum f_i |x_i - M|}{N}$. We have $M = 5$ and $N = 20$.

Let's calculate $\sum f_i |x_i - 5|$:

| $x_i$ | $f_i$ | $|x_i - M| = |x_i - 5|$ | $f_i |x_i - M|$ | | :---: | :---: | :-----------------------: | :-------------------: | | 3 | 5 | 2 | $5 \times 2 = 10$ | | 4 | 4 | 1 | $4 \times 1 = 4$ | | 5 | 4 | 0 | $4 \times 0 = 0$ | | 8 | 2 | 3 | $2 \times 3 = 6$ | | 10 | 2 | 5 | $2 \times 5 = 10$ | | 11 | 3 | 6 | $3 \times 6 = 18$ | | Total | 20 | | 48 |

$MD(M) = \frac{48}{20} = \frac{12}{5} = 2.4$.

So, (S) The mean deviation about the median is 2.4, which corresponds to (5) in List-II.

Step 6: Match the entries and select the correct option

Based on our calculations:

• (P) Mean is 6 $\rightarrow$ (3)
• (Q) Median is 5 $\rightarrow$ (2)
• (R) Mean deviation about mean is 2.7 $\rightarrow$ (4)
• (S) Mean deviation about median is 2.4 $\rightarrow$ (5)

The correct matching is $(P) \rightarrow(3) ~~ (Q) \rightarrow(2) ~~ (R) \rightarrow(4) ~~ (S) \rightarrow(5)$.

This corresponds to option A.