(b) The mean deviation about Mean for 1, 3, 5, 7, 9 is 2.4

Answer

To determine whether the mean deviation about the mean for the data set \(1, 3, 5, 7, 9\) is indeed \(2.4\), we will follow these steps:

### Step 1: Calculate the Mean
The mean (\(\mu\)) of a data set is calculated using the formula:
\[ \mu = \frac{\text{Sum of all observations}}{\text{Total number of observations}} \]
For our data set \(1, 3, 5, 7, 9\):
- Sum of observations = \(1 + 3 + 5 + 7 + 9 = 25\)
- Total number of observations = \(5\)

Thus, the mean is:
\[ \mu = \frac{25}{5} = 5 \]

### Step 2: Calculate the Absolute Deviations
Next, we need to calculate the absolute deviations of each observation from the mean:
\[ |x - \mu| \]
For each \(x\):
- For \(1\): \(|1 - 5| = | -4 | = 4\)
- For \(3\): \(|3 - 5| = | -2 | = 2\)
- For \(5\): \(|5 - 5| = |0| = 0\)
- For \(7\): \(|7 - 5| = |2| = 2\)
- For \(9\): \(|9 - 5| = |4| = 4\)

### Step 3: Sum of Absolute Deviations
Now, we sum these absolute deviations:
\[ \text{Sum of absolute deviations} = 4 + 2 + 0 + 2 + 4 = 12 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation using the formula:
\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Total number of observations}} \]
Substituting the values we have:
\[ \text{Mean Deviation} = \frac{12}{5} = 2.4 \]

### Conclusion
Thus, the mean deviation about the mean for the data set \(1, 3, 5, 7, 9\) is indeed \(2.4\), confirming the statement is correct.

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