The mean deviation from the mean for the set of observation -1, 0, 4 is

Options

A. `(2)/(3)`
B. 1
C. 2
D. `sqrt((14)/(3))`

Answer

To find the mean deviation from the mean for the set of observations -1, 0, and 4, we will follow these steps:

### Step 1: Calculate the Mean
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Total number of observations}} \]

For the given observations:
\[ \text{Sum} = -1 + 0 + 4 = 3 \]
The total number of observations is 3.

Thus, the mean is:
\[ \text{Mean} = \frac{3}{3} = 1 \]

### Step 2: Calculate the Absolute Deviations from the Mean
Next, we calculate the absolute deviations of each observation from the mean. The absolute deviation is given by:
\[ \text{Absolute Deviation} = |\text{Observation} - \text{Mean}| \]

Calculating for each observation:
- For -1:
\[ |-1 - 1| = |-2| = 2 \]
- For 0:
\[ |0 - 1| = |-1| = 1 \]
- For 4:
\[ |4 - 1| = |3| = 3 \]

### Step 3: Sum the Absolute Deviations
Now, we sum the absolute deviations:
\[ \text{Total Absolute Deviation} = 2 + 1 + 3 = 6 \]

### Step 4: Calculate the Mean Deviation
Finally, we calculate the mean deviation by dividing the total absolute deviation by the number of observations:
\[ \text{Mean Deviation} = \frac{\text{Total Absolute Deviation}}{\text{Total number of observations}} = \frac{6}{3} = 2 \]

### Final Answer
The mean deviation from the mean for the set of observations -1, 0, 4 is **2**.

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