The marks obtained by 9 students in a chemistry test are `50, 69, 20, 33, 53, 39, 40, 65 and 59`. If the mean deviation about the median of this data is `lambda`, then the value of `(9lambda)/(10)` is equal to

Answer

To solve the problem, we need to find the mean deviation about the median of the given marks and then calculate \( \frac{9\lambda}{10} \), where \( \lambda \) is the mean deviation.

### Step-by-Step Solution:

1. **List the Marks**:
The marks obtained by the students are:
\[ 50, 69, 20, 33, 53, 39, 40, 65, 59 \]

2. **Sort the Marks in Ascending Order**:
Arranging the marks in ascending order gives:
\[ 20, 33, 39, 40, 50, 53, 59, 65, 69 \]

3. **Find the Median**:
Since there are 9 students (an odd number), the median is the middle value, which is the 5th value in the sorted list:
\[ \text{Median} = 50 \]

4. **Calculate the Deviations from the Median**:
We calculate the absolute deviations from the median (50):
\[ |20 - 50| = 30 \\ |33 - 50| = 17 \\ |39 - 50| = 11 \\ |40 - 50| = 10 \\ |50 - 50| = 0 \\ |53 - 50| = 3 \\ |59 - 50| = 9 \\ |65 - 50| = 15 \\ |69 - 50| = 19 \]

5. **Sum of the Deviations**:
Now, we sum these absolute deviations:
\[ 30 + 17 + 11 + 10 + 0 + 3 + 9 + 15 + 19 = 114 \]

6. **Calculate the Mean Deviation**:
The mean deviation \( \lambda \) is given by the formula:
\[ \lambda = \frac{\text{Sum of Deviations}}{\text{Number of Students}} = \frac{114}{9} \]

7. **Calculate \( \frac{9\lambda}{10} \)**:
Now, we need to find \( \frac{9\lambda}{10} \):
\[ \frac{9\lambda}{10} = \frac{9 \times \frac{114}{9}}{10} = \frac{114}{10} = 11.4 \]

### Final Answer:
\[ \frac{9\lambda}{10} = 11.4 \]