Following are the marks obtained by 9 student in a mathematics test
50,69,20,33,53,39,40,65,59,
The mean deviation from the median is

Options

A. 9
B. 10.5
C. 12.67
D. 14.76

Explanation

To solve the problem of finding the mean deviation from the median for the given marks, we will follow these steps:

### Step 1: Arrange the Data in Ascending Order
The marks obtained by the students are:
50, 69, 20, 33, 53, 39, 40, 65, 59.

Arranging these in ascending order:
20, 33, 39, 40, 50, 53, 59, 65, 69.

### Step 2: Calculate the Median
To find the median, we need to identify the middle value in the ordered list. Since there are 9 observations (an odd number), the median is the value at the position \((n + 1) / 2\), where \(n\) is the number of observations.

\[ \text{Median position} = \frac{9 + 1}{2} = 5 \]

The 5th value in the ordered list is 50. Therefore, the median is:
\[ \text{Median} = 50 \]

### Step 3: Calculate the Deviations from the Median
Next, we calculate the absolute deviations from the median (50) for each mark:

- For 20: \(|20 - 50| = 30\)
- For 33: \(|33 - 50| = 17\)
- For 39: \(|39 - 50| = 11\)
- For 40: \(|40 - 50| = 10\)
- For 50: \(|50 - 50| = 0\)
- For 53: \(|53 - 50| = 3\)
- For 59: \(|59 - 50| = 9\)
- For 65: \(|65 - 50| = 15\)
- For 69: \(|69 - 50| = 19\)

The deviations are:
30, 17, 11, 10, 0, 3, 9, 15, 19.

### Step 4: Calculate the Mean Deviation
Now, we sum up all the absolute deviations and divide by the number of observations (9):

\[ \text{Sum of deviations} = 30 + 17 + 11 + 10 + 0 + 3 + 9 + 15 + 19 = 114 \]

Now, we calculate the mean deviation:
\[ \text{Mean Deviation} = \frac{\text{Sum of deviations}}{n} = \frac{114}{9} \approx 12.67 \]

### Final Answer
The mean deviation from the median is approximately:
\[ \text{Mean Deviation} \approx 12.67 \]

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