The problem in the image asks to find the mean deviation about the mean for the data set:

Data: 4, 7, 6, 9, 10, 12, 13, 17

Let's solve this step by step:

Step 1: Find the Mean of the Data

The formula for the mean $\bar{x}$ is:

$\bar{x} = \frac{\sum x_i}{n}$

Where $x_i$ are the data values, and $n$ is the number of data points.

$\bar{x} = \frac{4 + 7 + 6 + 9 + 10 + 12 + 13 + 17}{8} = \frac{78}{8} = 9.75$

Step 2: Calculate the Absolute Deviations

Now, subtract the mean from each data point and take the absolute value:

$|4 - 9.75| = 5.75, \quad |7 - 9.75| = 2.75, \quad |6 - 9.75| = 3.75, \quad |9 - 9.75| = 0.75$ $|10 - 9.75| = 0.25, \quad |12 - 9.75| = 2.25, \quad |13 - 9.75| = 3.25, \quad |17 - 9.75| = 7.25$

Step 3: Calculate the Mean Deviation

The formula for mean deviation about the mean is:

$\text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{n}$

Now sum the absolute deviations:

$5.75 + 2.75 + 3.75 + 0.75 + 0.25 + 2.25 + 3.25 + 7.25 = 26$

Finally, divide by the number of data points $n = 8$:

$\text{Mean Deviation} = \frac{26}{8} = 3.25$

Final Answer:

The mean deviation about the mean is 3.25.

None of the options listed (8, 9, 3) match this answer, so the correct choice is:

Option D: None of these

Would you like a detailed explanation of any step or have any other questions?

Related Questions:

1. What is the difference between mean deviation about the mean and mean deviation about the median?
2. How is standard deviation different from mean deviation?
3. What happens if we take the square of deviations instead of absolute values?
4. Can you compute mean deviation for grouped data?
5. How do outliers affect mean deviation compared to other measures of dispersion?

Tip:

When calculating mean deviation, remember to always use the absolute values of the differences from the mean, never squared values.