The mean deviation of the data 2, 9, 9, 3, 6, 9, 4 from the mean is:

Question

Accepted Answer

To determine the mean deviation of the data set 2, 9, 9, 3, 6, 9, 4 from the mean, we need to follow these steps:

1. **Calculate the Mean of the Data:**
   - Sum of the data: $2 + 9 + 9 + 3 + 6 + 9 + 4 = 42$
   - Number of data points: 7
   - Mean ($\bar{x}$) = $\frac{42}{7} = 6$

2. **Calculate the Deviations from the Mean:**
   - Deviations: $|2 - 6|, |9 - 6|, |9 - 6|, |3 - 6|, |6 - 6|, |9 - 6|, |4 - 6|$
   - Deviations: 4, 3, 3, 3, 0, 3, 2

3. **Calculate the Mean Deviation:**
   - Sum of deviations: $4 + 3 + 3 + 3 + 0 + 3 + 2 = 18$
   - Mean deviation = $\frac{18}{7} \approx 2.57$

Thus, the mean deviation of the data from the mean is approximately 2.57, which corresponds to Option 2.

**Explanation for Why Other Options are Incorrect:**

- **Option 1 (0):** This option suggests that the mean deviation is zero, which would imply that all data points are equal to the mean. Since the data points vary and are not all equal to the mean, this option is incorrect.

- **Option 3 (1.57):** This option underestimates the mean deviation. The calculated mean deviation is 2.57, not 1.57. Therefore, this option is incorrect.

- **Option 4 (3.57):** This option overestimates the mean deviation. The calculated mean deviation is 2.57, not 3.57. Therefore, this option is incorrect.

In conclusion, the correct answer is Option 2, as the calculated mean deviation of the data from the mean is approximately 2.57.