The mean deviation of the data 4,5,7,8,9,10,6 from the median is

Options

A. 1.87
B. 2.32
C. 1.71
D. 2.45

Answer

To find the mean deviation of the data set \(4, 5, 6, 7, 8, 9, 10\) from the median, we will follow these steps:

### Step 1: Arrange the data in ascending order
The data is already given as \(4, 5, 6, 7, 8, 9, 10\).

### Step 2: Find the number of data points (N)
Count the number of data points:
- \(N = 7\)

### Step 3: Calculate the median
Since \(N\) is odd, the median is the middle value. The median can be found using the formula:
\[ \text{Median} = \frac{N + 1}{2} \text{th term} \]
Substituting the value of \(N\):
\[ \text{Median} = \frac{7 + 1}{2} = \frac{8}{2} = 4 \text{th term} \]
The 4th term in the ordered data is \(7\). Therefore, the median is:
\[ \text{Median} = 7 \]

### Step 4: Calculate the absolute deviations from the median
We will calculate the absolute deviations of each data point from the median:
- For \(4\): \(|4 - 7| = 3\)
- For \(5\): \(|5 - 7| = 2\)
- For \(6\): \(|6 - 7| = 1\)
- For \(7\): \(|7 - 7| = 0\)
- For \(8\): \(|8 - 7| = 1\)
- For \(9\): \(|9 - 7| = 2\)
- For \(10\): \(|10 - 7| = 3\)

### Step 5: Sum the absolute deviations
Now, we sum all the absolute deviations:
\[ \text{Sum} = 3 + 2 + 1 + 0 + 1 + 2 + 3 = 12 \]

### Step 6: Calculate the mean deviation
The mean deviation is calculated by dividing the sum of the absolute deviations by the number of data points \(N\):
\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{N} = \frac{12}{7} \approx 1.71 \]

### Final Answer
The mean deviation of the data from the median is approximately \(1.71\).

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