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 (\( \bar{x} \))
The mean 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. First, sum the data points:
\[ 3 + 10 + 10 + 4 + 7 + 10 + 5 = 49 \]

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

3. Now, calculate the mean:
\[ \bar{x} = \frac{49}{7} = 7 \]

### Step 2: Calculate the Absolute Deviations from the Mean
Next, we calculate the absolute deviations from the mean for each data point:

\[ |x_i - \bar{x}| \]

- For \(3\): \(|3 - 7| = 4\)
- For \(10\): \(|10 - 7| = 3\)
- For \(10\): \(|10 - 7| = 3\)
- For \(4\): \(|4 - 7| = 3\)
- For \(7\): \(|7 - 7| = 0\)
- For \(10\): \(|10 - 7| = 3\)
- For \(5\): \(|5 - 7| = 2\)

### Step 3: Sum the Absolute Deviations
Now, we sum 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 using the formula:

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

Substituting the values we have:

\[ \text{Mean Deviation} = \frac{18}{7} \approx 2.57 \]

### Final Answer
The mean deviation of the data \(3, 10, 10, 4, 7, 10, 5\) from the mean is approximately \(2.57\).

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