The standard deviation of the observation 5, 5, 5, 5, 5 is

Options

A. 0
B. 5
C. 20
D. 25

Explanation

To find the standard deviation of the observations 5, 5, 5, 5, and 5, we will follow these steps:

### Step 1: Identify the observations
The given observations are:
\[ 5, 5, 5, 5, 5 \]

### Step 2: Calculate the mean
The mean (average) is calculated using the formula:
\[ \text{Mean} = \frac{\text{Sum of observations}}{\text{Number of observations}} \]
Calculating the sum:
\[ 5 + 5 + 5 + 5 + 5 = 25 \]
Now, divide by the number of observations (which is 5):
\[ \text{Mean} = \frac{25}{5} = 5 \]

### Step 3: Calculate the deviations from the mean
Next, we find the deviations of each observation from the mean:
\[ \text{Deviations} = \text{Observation} - \text{Mean} \]
For all observations:
\[ 5 - 5 = 0 \]
Thus, the deviations are:
\[ 0, 0, 0, 0, 0 \]

### Step 4: Square the deviations
Now, we square each of the deviations:
\[ 0^2 = 0 \]
So the squared deviations are:
\[ 0, 0, 0, 0, 0 \]

### Step 5: Calculate the variance
The variance is the average of the squared deviations. We calculate it using the formula:
\[ \text{Variance} = \frac{\text{Sum of squared deviations}}{\text{Number of observations}} \]
Calculating the sum of squared deviations:
\[ 0 + 0 + 0 + 0 + 0 = 0 \]
Now, divide by the number of observations:
\[ \text{Variance} = \frac{0}{5} = 0 \]

### Step 6: Calculate the standard deviation
The standard deviation is the square root of the variance:
\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{0} = 0 \]

### Final Answer
Thus, the standard deviation of the observations 5, 5, 5, 5, and 5 is:
\[ \boxed{0} \]