What is the mean deviation of the data 2, 9, 9, 3, 6, 9, 4 ?

Options

A. 2.23
B. 2.57
C. 3.23
D. 3.57

Explanation

To find the mean deviation of the data set \(2, 9, 9, 3, 6, 9, 4\), we will follow these steps:

### Step 1: Calculate the Mean
First, we need to find the mean of the data set. The mean is calculated by taking the sum of all observations and dividing it by the number of observations.

1. **Sum of the observations**:
\[ 2 + 9 + 9 + 3 + 6 + 9 + 4 = 42 \]

2. **Number of observations**:
There are 7 observations.

3. **Mean**:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} = \frac{42}{7} = 6 \]

### Step 2: Calculate the Deviations from the Mean
Next, we will find the absolute deviations of each observation from the mean.

1. **Deviations**:
- For \(2\): \(|2 - 6| = 4\)
- For \(9\): \(|9 - 6| = 3\)
- For \(9\): \(|9 - 6| = 3\)
- For \(3\): \(|3 - 6| = 3\)
- For \(6\): \(|6 - 6| = 0\)
- For \(9\): \(|9 - 6| = 3\)
- For \(4\): \(|4 - 6| = 2\)

### Step 3: Sum of the Absolute Deviations
Now, we will 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 will 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 set \(2, 9, 9, 3, 6, 9, 4\) is approximately \(2.57\).

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