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. 3.57

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
The mean (\(\bar{x}\)) is calculated using the formula:
\[ \bar{x} = \frac{\sum x_i}{n} \]
where \(x_i\) are the data points and \(n\) is the number of observations.

1. **Sum the data points**:
\[ 3 + 10 + 10 + 4 + 7 + 10 + 5 = 49 \]

2. **Count the number of observations**:
\[ n = 7 \]

3. **Calculate the mean**:
\[ \bar{x} = \frac{49}{7} = 7 \]

### Step 2: Calculate the Deviations from the Mean
Next, we calculate the absolute deviations from the mean for each data point:
\[ d_i = |x_i - \bar{x}| \]

1. For \(x_1 = 3\):
\[ d_1 = |3 - 7| = 4 \]

2. For \(x_2 = 10\):
\[ d_2 = |10 - 7| = 3 \]

3. For \(x_3 = 10\):
\[ d_3 = |10 - 7| = 3 \]

4. For \(x_4 = 4\):
\[ d_4 = |4 - 7| = 3 \]

5. For \(x_5 = 7\):
\[ d_5 = |7 - 7| = 0 \]

6. For \(x_6 = 10\):
\[ d_6 = |10 - 7| = 3 \]

7. For \(x_7 = 5\):
\[ d_7 = |5 - 7| = 2 \]

### Step 3: Sum the Absolute Deviations
Now, we sum all the absolute deviations:
\[ \sum d_i = 4 + 3 + 3 + 3 + 0 + 3 + 2 = 18 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation using the formula:
\[ \text{Mean Deviation} = \frac{\sum d_i}{n} \]
Substituting the values we have:
\[ \text{Mean Deviation} = \frac{18}{7} \approx 2.57 \]

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

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