Mean deviation from the mean for data 6, 7 10, 12, 13, 4, 8, 12 is

Options

A. 2.35
B. 2.75
C. 3.35
D. 3.75

Answer

To find the mean deviation from the mean for the given data set \(6, 7, 10, 12, 13, 4, 8, 12\), we will follow these steps:

### Step 1: Calculate the Mean
First, we need to find the mean of the data set.

\[ \text{Mean} (x̄) = \frac{\sum x}{n} \]

Where:
- \(\sum x\) is the sum of all data points.
- \(n\) is the number of data points.

Calculating \(\sum x\):

\[ \sum x = 6 + 7 + 10 + 12 + 13 + 4 + 8 + 12 = 72 \]

Now, we find \(n\):

\[ n = 8 \]

Now, we can calculate the mean:

\[ x̄ = \frac{72}{8} = 9 \]

### Step 2: Calculate the Absolute Deviations
Next, we will calculate the absolute deviations from the mean for each data point. The absolute deviation is given by \(|x_i - x̄|\).

\[ \begin{align*} |6 - 9| & = 3 \\ |7 - 9| & = 2 \\ |10 - 9| & = 1 \\ |12 - 9| & = 3 \\ |13 - 9| & = 4 \\ |4 - 9| & = 5 \\ |8 - 9| & = 1 \\ |12 - 9| & = 3 \\ \end{align*} \]

### Step 3: Sum of Absolute Deviations
Now, we will sum all the absolute deviations:

\[ \text{Sum of absolute deviations} = 3 + 2 + 1 + 3 + 4 + 5 + 1 + 3 = 22 \]

### Step 4: Calculate the Mean Deviation
Finally, we can calculate the mean deviation using the formula:

\[ \text{Mean Deviation} = \frac{\sum |x_i - x̄|}{n} \]

Substituting the values we have:

\[ \text{Mean Deviation} = \frac{22}{8} = 2.75 \]

### Conclusion
The mean deviation from the mean for the data set \(6, 7, 10, 12, 13, 4, 8, 12\) is \(2.75\).