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

Options

A. `(49)/(7)`
B. `(19)/(7)`
C. `(50)/(7)`
D. `(18)/(7)`

Answer

To find the mean deviation of the data set \(3, 10, 10, 4, 7, 10, 5\), 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 data points.

1. **Sum the data points**:
\[ 3 + 10 + 10 + 4 + 7 + 10 + 5 = 49 \]
2. **Count the number of data points**:
\[ n = 7 \]
3. **Calculate the mean**:
\[ \bar{x} = \frac{49}{7} = 7 \]

### Step 2: Calculate the Mean Deviation
The mean deviation is calculated using the formula:
\[ \text{Mean Deviation} = \frac{\sum |x_i - \bar{x}|}{n} \]
where \(|x_i - \bar{x}|\) is the absolute deviation of each data point from the mean.

1. **Calculate the absolute deviations**:
- For \(x_1 = 3\):
\[ |3 - 7| = | -4 | = 4 \]
- For \(x_2 = 10\):
\[ |10 - 7| = | 3 | = 3 \]
- For \(x_3 = 10\):
\[ |10 - 7| = | 3 | = 3 \]
- For \(x_4 = 4\):
\[ |4 - 7| = | -3 | = 3 \]
- For \(x_5 = 7\):
\[ |7 - 7| = | 0 | = 0 \]
- For \(x_6 = 10\):
\[ |10 - 7| = | 3 | = 3 \]
- For \(x_7 = 5\):
\[ |5 - 7| = | -2 | = 2 \]

2. **Sum of absolute deviations**:
\[ 4 + 3 + 3 + 3 + 0 + 3 + 2 = 18 \]

3. **Calculate the mean deviation**:
\[ \text{Mean Deviation} = \frac{18}{7} \approx 2.57 \]

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

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