The mean deviation of the data 2,7,9,11,15,16 from the median is

Options

A. 3
B. 4
C. 5
D. 6

Answer

To find the mean deviation of the data set \(2, 7, 9, 11, 15, 16\) from the median, we will follow these steps:

### Step 1: Arrange the Data
The data is already given in ascending order:
\[ 2, 7, 9, 11, 15, 16 \]

### Step 2: Find the Median
Since the number of observations \(n = 6\) (which is even), the median is calculated as the average of the \(n/2\)th and \((n/2 + 1)\)th terms.

- The \(n/2\)th term (3rd term) is \(9\).
- The \((n/2 + 1)\)th term (4th term) is \(11\).

Now, calculate the median:
\[ \text{Median} = \frac{\text{3rd term} + \text{4th term}}{2} = \frac{9 + 11}{2} = \frac{20}{2} = 10 \]

### Step 3: Calculate the Absolute Deviations from the Median
Next, we find the absolute deviations of each data point from the median (10):
- For \(2\): \(|2 - 10| = 8\)
- For \(7\): \(|7 - 10| = 3\)
- For \(9\): \(|9 - 10| = 1\)
- For \(11\): \(|11 - 10| = 1\)
- For \(15\): \(|15 - 10| = 5\)
- For \(16\): \(|16 - 10| = 6\)

### Step 4: Sum the Absolute Deviations
Now, sum all the absolute deviations:
\[ 8 + 3 + 1 + 1 + 5 + 6 = 24 \]

### Step 5: Calculate the Mean Deviation
Finally, divide the total absolute deviation by the number of observations to find the mean deviation:
\[ \text{Mean Deviation} = \frac{\text{Total Absolute Deviations}}{n} = \frac{24}{6} = 4 \]

### Final Answer
The mean deviation of the data from the median is \(4\).

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