If standard deviation of 1,2,3,4,….,10 is `sigma` then standard deviation of 11, 12, …20 is

Options

A. `sigma + 10`
B. `10 sigma`
C. `sigma`
D. `5 sigma`

Answer

To solve the problem of finding the standard deviation of the numbers 11, 12, ..., 20 given that the standard deviation of the numbers 1, 2, 3, ..., 10 is `σ`, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Original Set of Numbers**:
The original set of numbers is 1, 2, 3, 4, ..., 10.

2. **Calculate the Standard Deviation of the Original Set**:
We know that the standard deviation of the numbers 1, 2, 3, 4, ..., 10 is given as `σ`.

3. **Transform the New Set of Numbers**:
The new set of numbers is 11, 12, 13, ..., 20. We can express these numbers in terms of the original set:
- 11 = 1 + 10
- 12 = 2 + 10
- 13 = 3 + 10
- ...
- 20 = 10 + 10

4. **Understand the Effect of Adding a Constant**:
When we add a constant (in this case, 10) to each number in the original set, the standard deviation remains unchanged. This is a property of standard deviation: adding or subtracting a constant to all values does not affect the spread of the data.

5. **Conclude the Standard Deviation of the New Set**:
Since we have added a constant (10) to all the numbers in the original set, the standard deviation of the new set (11, 12, ..., 20) will also be `σ`.

### Final Answer:
The standard deviation of the numbers 11, 12, ..., 20 is `σ`.