Statement-1 : if the S.D. of a variable x is 6, then the S.D. of ax +b is |a| 6.
Statement-2 : The variance and S.D. is not independent of change of scale

Answer

To solve the problem, we need to analyze the two statements provided and determine their validity.

### Step 1: Analyze Statement 1
**Statement 1**: If the standard deviation (S.D.) of a variable \( x \) is 6, then the S.D. of \( ax + b \) is \( |a| \times 6 \).

**Explanation**:
- The standard deviation measures the dispersion of a set of values.
- When we apply a linear transformation to the variable \( x \) in the form \( ax + b \):
- The constant \( b \) does not affect the standard deviation; it only shifts the data.
- The coefficient \( a \) scales the data. Thus, the standard deviation of \( ax + b \) is affected by the absolute value of \( a \).

Mathematically, if \( \sigma_x \) is the standard deviation of \( x \), then:
\[ \sigma_{ax + b} = |a| \cdot \sigma_x \]
Given that \( \sigma_x = 6 \):
\[ \sigma_{ax + b} = |a| \cdot 6 \]
Thus, **Statement 1 is true**.

### Step 2: Analyze Statement 2
**Statement 2**: The variance and S.D. are not independent of the change of scale.

**Explanation**:
- Variance is the square of the standard deviation. When we change the scale of the data (for example, multiplying by a constant \( a \)):
- The variance of \( ax + b \) becomes:
\[ \text{Var}(ax + b) = a^2 \cdot \text{Var}(x) \]
- This shows that variance is affected by the square of the scaling factor \( a \).
- Since the standard deviation is the square root of variance, it also shows dependence on the change of scale.

Thus, **Statement 2 is also true**.

### Conclusion
Both statements are true:
- **Statement 1** is true: The S.D. of \( ax + b \) is \( |a| \times 6 \).
- **Statement 2** is true: Variance and S.D. are not independent of the change of scale.

### Final Answer
Both statements are true.

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