The mean deviation of the data 3,10,10,4,7,10,5 from the mean is

Options

A. 2
B. 2.57
C. 3
D. 3.75

Explanation

To find the mean deviation of the data set \(3, 10, 10, 4, 7, 10, 5\) from the mean, we will follow these steps:

### Step 1: Calculate the Mean
First, we need to calculate the mean (\(\bar{x}\)) of the data.

\[ \bar{x} = \frac{\text{Sum of all observations}}{\text{Number of observations}} = \frac{3 + 10 + 10 + 4 + 7 + 10 + 5}{7} \]

Calculating the sum:

\[ 3 + 10 + 10 + 4 + 7 + 10 + 5 = 49 \]

Now, divide by the number of observations (which is 7):

\[ \bar{x} = \frac{49}{7} = 7 \]

### Step 2: Calculate the Deviations from the Mean
Next, we calculate the absolute deviations from the mean for each observation. The deviation is calculated as \( |x_i - \bar{x}| \).

\[ \begin{align*} |3 - 7| & = 4 \\ |10 - 7| & = 3 \\ |10 - 7| & = 3 \\ |4 - 7| & = 3 \\ |7 - 7| & = 0 \\ |10 - 7| & = 3 \\ |5 - 7| & = 2 \\ \end{align*} \]

### Step 3: Sum of Absolute Deviations
Now, we sum up all the absolute deviations calculated in the previous step:

\[ \text{Sum of absolute deviations} = 4 + 3 + 3 + 3 + 0 + 3 + 2 = 18 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation by dividing the sum of absolute deviations by the number of observations:

\[ \text{Mean Deviation} = \frac{\text{Sum of absolute deviations}}{\text{Number of observations}} = \frac{18}{7} \approx 2.57 \]

### Conclusion
The mean deviation of the data from the mean is approximately \(2.57\).

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