Find the M.D. from median of the following distribution : 3,9,2,8,1,7,7,3.

Answer

To find the Mean Deviation (M.D.) from the median of the given distribution, we will follow these steps:

### Step 1: Arrange the data in ascending order
The given data is: 3, 9, 2, 8, 1, 7, 7, 3.

**Ascending order:** 1, 2, 3, 3, 7, 7, 8, 9.

### Step 2: Find the median
To find the median, we first determine the number of observations. There are 8 numbers in total.

Since the number of observations (n) is even, the median is calculated as:
\[ \text{Median} = \frac{\text{Value at position } \frac{n}{2} + \text{Value at position } \frac{n}{2} + 1}{2} \]
Here, \(n = 8\), so we find the 4th and 5th values:
- 4th value = 3
- 5th value = 7

Thus,
\[ \text{Median} = \frac{3 + 7}{2} = \frac{10}{2} = 5. \]

### Step 3: Calculate the absolute deviations from the median
Next, we will find the absolute deviations of each data point from the median (5):
- \( |5 - 1| = 4 \)
- \( |5 - 2| = 3 \)
- \( |5 - 3| = 2 \)
- \( |5 - 3| = 2 \)
- \( |5 - 7| = 2 \)
- \( |5 - 7| = 2 \)
- \( |5 - 8| = 3 \)
- \( |5 - 9| = 4 \)

### Step 4: Sum the absolute deviations
Now, we sum all the absolute deviations:
\[ 4 + 3 + 2 + 2 + 2 + 2 + 3 + 4 = 22. \]

### Step 5: Calculate the Mean Deviation
Finally, we calculate the Mean Deviation (M.D.) by dividing the total absolute deviation by the number of observations:
\[ \text{M.D.} = \frac{\text{Total Absolute Deviation}}{n} = \frac{22}{8} = \frac{11}{4} = 2.75. \]

### Final Answer
The Mean Deviation from the median of the given distribution is **2.75**.

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