Find the mean deviation about the median for the following data
13,17,16,11,13,10,16,11,18,12,17

Answer

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

### Step 1: Arrange the data in ascending order
The given data is:
13, 17, 16, 11, 13, 10, 16, 11, 18, 12, 17

Arranging it in ascending order, we get:
10, 11, 11, 12, 13, 13, 16, 16, 17, 17, 18

### Step 2: Find the median
To find the median, we first determine the number of observations (n). Here, n = 11 (since there are 11 data points).

The median is the value at the (n + 1)/2 position.
So, (11 + 1)/2 = 6th position.

Looking at our ordered data:
10, 11, 11, 12, 13, **13**, 16, 16, 17, 17, 18

The median is 13.

### Step 3: Calculate the mean deviation about the median
The mean deviation is calculated using the formula:
\[ \text{Mean Deviation} = \frac{1}{n} \sum |x_i - m| \]
where \( m \) is the median and \( x_i \) are the data points.

Now, we will calculate the absolute deviations from the median (13):
- |10 - 13| = 3
- |11 - 13| = 2
- |11 - 13| = 2
- |12 - 13| = 1
- |13 - 13| = 0
- |13 - 13| = 0
- |16 - 13| = 3
- |16 - 13| = 3
- |17 - 13| = 4
- |17 - 13| = 4
- |18 - 13| = 5

Now, we sum these absolute deviations:
\[ 3 + 2 + 2 + 1 + 0 + 0 + 3 + 3 + 4 + 4 + 5 = 27 \]

### Step 4: Calculate the mean deviation
Now we divide the total absolute deviation by the number of observations (n = 11):
\[ \text{Mean Deviation} = \frac{27}{11} \approx 2.45 \]

### Final Answer
The mean deviation about the median for the given data is approximately **2.45**.

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