The mean deviation about the median of the following distribution is
`{:("Marks obtained",10,11,12,14,15),("Number of students",2,3,8,3,4):}`

Explanation

To find the mean deviation about the median for the given distribution, we will follow these steps:

### Step 1: Create the Frequency Table
We have the following data:

| Marks Obtained (xi) | Number of Students (fi) |
|----------------------|-------------------------|
| 10 | 2 |
| 11 | 3 |
| 12 | 8 |
| 14 | 3 |
| 15 | 4 |

### Step 2: Calculate Cumulative Frequency
We will calculate the cumulative frequency (cf):

| Marks Obtained (xi) | Number of Students (fi) | Cumulative Frequency (cf) |
|----------------------|-------------------------|----------------------------|
| 10 | 2 | 2 |
| 11 | 3 | 5 |
| 12 | 8 | 13 |
| 14 | 3 | 16 |
| 15 | 4 | 20 |

### Step 3: Find the Total Frequency
The total frequency \( N \) is the last cumulative frequency value, which is 20.

### Step 4: Calculate the Median
To find the median, we calculate \( \frac{N}{2} = \frac{20}{2} = 10 \). We find the cumulative frequency that is just greater than or equal to 10. This corresponds to the value 12.

Thus, the median \( M \) is 12.

### Step 5: Calculate Deviations
Now we will calculate the deviations \( d_i = x_i - M \):

| Marks Obtained (xi) | Number of Students (fi) | Deviation (di = xi - M) |
|----------------------|-------------------------|--------------------------|
| 10 | 2 | 10 - 12 = -2 |
| 11 | 3 | 11 - 12 = -1 |
| 12 | 8 | 12 - 12 = 0 |
| 14 | 3 | 14 - 12 = 2 |
| 15 | 4 | 15 - 12 = 3 |

### Step 6: Calculate \( f_i \cdot d_i \)
Now we will calculate \( f_i \cdot d_i \):

| Marks Obtained (xi) | Number of Students (fi) | Deviation (di) | \( f_i \cdot d_i \) |
|----------------------|-------------------------|-----------------|----------------------|
| 10 | 2 | -2 | 2 * -2 = -4 |
| 11 | 3 | -1 | 3 * -1 = -3 |
| 12 | 8 | 0 | 8 * 0 = 0 |
| 14 | 3 | 2 | 3 * 2 = 6 |
| 15 | 4 | 3 | 4 * 3 = 12 |

### Step 7: Sum of \( f_i \cdot d_i \)
Now we sum up the values of \( f_i \cdot d_i \):

\[ \sum f_i \cdot d_i = -4 - 3 + 0 + 6 + 12 = 11 \]

### Step 8: Calculate Mean Deviation
Finally, we calculate the mean deviation about the median using the formula:

\[ \text{Mean Deviation} = \frac{\sum f_i \cdot d_i}{N} = \frac{11}{20} = 0.55 \]

### Final Answer
The mean deviation about the median is **0.55**.

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