Find the mean deviation of the first three odd natural numbers from their mean.

Answer

To find the mean deviation of the first three odd natural numbers from their mean, we will follow these steps:

### Step 1: Identify the first three odd natural numbers.
The first three odd natural numbers are:
1, 3, and 5.

### Step 2: Calculate the mean (μ) of these numbers.
The mean (μ) is calculated using the formula:
\[ \mu = \frac{\text{Sum of the numbers}}{\text{Total count of numbers}} \]
So, we calculate:
\[ \mu = \frac{1 + 3 + 5}{3} = \frac{9}{3} = 3 \]

### Step 3: Calculate the mean deviation.
The mean deviation is defined as:
\[ \text{Mean Deviation} = \frac{\sum |x_i - \mu|}{n} \]
Where \(x_i\) are the values, \(\mu\) is the mean, and \(n\) is the number of values.

Now we will calculate \(|x_i - \mu|\) for each number:
- For \(x_1 = 1\):
\[ |1 - 3| = | -2 | = 2 \]
- For \(x_2 = 3\):
\[ |3 - 3| = |0| = 0 \]
- For \(x_3 = 5\):
\[ |5 - 3| = |2| = 2 \]

### Step 4: Sum the absolute deviations.
Now we sum these absolute deviations:
\[ \sum |x_i - \mu| = 2 + 0 + 2 = 4 \]

### Step 5: Divide by the number of values to find the mean deviation.
Now we divide the sum of absolute deviations by the number of values (n = 3):
\[ \text{Mean Deviation} = \frac{4}{3} \]

### Final Answer:
The mean deviation of the first three odd natural numbers from their mean is \(\frac{4}{3}\).

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