Mean deviation of first three odd numbers from mean is

Options

A. 3
B. 2
C. 1
D. `4//3`

Answer

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

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

### Step 2: Calculate the mean (average) of these numbers.
To calculate the mean, we use the formula:
\[ \text{Mean} (x̄) = \frac{\text{Sum of the numbers}}{\text{Total number of terms}} \]
Calculating the sum:
\[ 1 + 3 + 5 = 9 \]
Now, divide by the total number of terms (which is 3):
\[ x̄ = \frac{9}{3} = 3 \]

### Step 3: Calculate the absolute deviations from the mean.
Now, we will find the absolute deviations of each number from the mean (3):
- For 1:
\[ |1 - 3| = | -2 | = 2 \]
- For 3:
\[ |3 - 3| = |0| = 0 \]
- For 5:
\[ |5 - 3| = |2| = 2 \]

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

### Step 5: Calculate the mean deviation.
Finally, we calculate the mean deviation using the formula:
\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Total number of terms}} \]
Substituting the values we found:
\[ \text{Mean Deviation} = \frac{4}{3} \]

### Conclusion
The mean deviation of the first three odd numbers from their mean is:
\[ \frac{4}{3} \]

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