Find the mean deviation of first 7 natural numbers from their mean.

Answer

To find the mean deviation of the first 7 natural numbers from their mean, we can follow these steps:

### Step 1: Identify the first 7 natural numbers.
The first 7 natural numbers are:
1, 2, 3, 4, 5, 6, 7.

### Step 2: Calculate the mean of these numbers.
The mean (μ) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} \]
Calculating the sum:
\[ 1 + 2 + 3 + 4 + 5 + 6 + 7 = 28 \]
Now, divide by the number of values (which is 7):
\[ \text{Mean} = \frac{28}{7} = 4 \]

### Step 3: Calculate the absolute deviations from the mean.
Now, we need to find the absolute deviations of each number from the mean (4):
- |1 - 4| = 3
- |2 - 4| = 2
- |3 - 4| = 1
- |4 - 4| = 0
- |5 - 4| = 1
- |6 - 4| = 2
- |7 - 4| = 3

### Step 4: Calculate the mean of these absolute deviations.
Now, we will sum the absolute deviations:
\[ 3 + 2 + 1 + 0 + 1 + 2 + 3 = 12 \]
Now, divide by the number of values (7):
\[ \text{Mean Deviation} = \frac{12}{7} \approx 1.7143 \]

### Final Answer:
The mean deviation of the first 7 natural numbers from their mean is approximately \(1.7143\).