The standard deviation of the set `{10,10,10,10,10}` is
(A) 0
(B) 1
(C ) 5
(D) 10

Options

A. C
B. A
C. B
D. D

Answer

To find the standard deviation of the set `{10, 10, 10, 10, 10}`, we can follow these steps:

### Step 1: Calculate the Mean
First, we need to calculate the mean (average) of the numbers in the set.

\[ \text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}} = \frac{10 + 10 + 10 + 10 + 10}{5} = \frac{50}{5} = 10 \]

### Step 2: Calculate the Variance
Next, we calculate the variance. The variance is the average of the squared differences from the mean.

1. Find the differences from the mean for each number:
- \(10 - 10 = 0\)
- \(10 - 10 = 0\)
- \(10 - 10 = 0\)
- \(10 - 10 = 0\)
- \(10 - 10 = 0\)

2. Square each difference:
- \(0^2 = 0\)
- \(0^2 = 0\)
- \(0^2 = 0\)
- \(0^2 = 0\)
- \(0^2 = 0\)

3. Calculate the average of these squared differences:
\[ \text{Variance} = \frac{0 + 0 + 0 + 0 + 0}{5} = \frac{0}{5} = 0 \]

### Step 3: Calculate the Standard Deviation
The standard deviation is the square root of the variance.

\[ \text{Standard Deviation} = \sqrt{\text{Variance}} = \sqrt{0} = 0 \]

### Conclusion
The standard deviation of the set `{10, 10, 10, 10, 10}` is **0**.

### Answer
Thus, the correct option is (A) 0.

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