The mean deviation about the mean for 3,8,4,10,6 is :

Options

A. 2
B. 2.24
C. 3
D. 3.5

Answer

To find the mean deviation about the mean for the data set \(3, 8, 4, 10, 6\), we will follow these steps:

### Step 1: Calculate the Mean
The mean (\( \bar{x} \)) is calculated using the formula:
\[ \bar{x} = \frac{\sum x_i}{n} \]
where \( \sum x_i \) is the sum of all observations and \( n \) is the number of observations.

**Calculating the sum:**
\[ \sum x_i = 3 + 8 + 4 + 10 + 6 = 31 \]
**Number of observations:**
\[ n = 5 \]
**Calculating the mean:**
\[ \bar{x} = \frac{31}{5} = 6.2 \]

### Step 2: Calculate the Absolute Deviations
Next, we find the absolute deviations of each observation from the mean:
\[ |x_i - \bar{x}| \]
Calculating each deviation:
- For \(3\):
\[ |3 - 6.2| = | -3.2 | = 3.2 \]
- For \(8\):
\[ |8 - 6.2| = |1.8| = 1.8 \]
- For \(4\):
\[ |4 - 6.2| = |-2.2| = 2.2 \]
- For \(10\):
\[ |10 - 6.2| = |3.8| = 3.8 \]
- For \(6\):
\[ |6 - 6.2| = |-0.2| = 0.2 \]

### Step 3: Sum of Absolute Deviations
Now, we sum all the absolute deviations:
\[ \sum |x_i - \bar{x}| = 3.2 + 1.8 + 2.2 + 3.8 + 0.2 = 11.2 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation (\(MD\)) using the formula:
\[ MD = \frac{\sum |x_i - \bar{x}|}{n} \]
Substituting the values:
\[ MD = \frac{11.2}{5} = 2.24 \]

### Conclusion
The mean deviation about the mean for the data set \(3, 8, 4, 10, 6\) is \(2.24\).

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