The standard deviation of 50 values of a variable x is 15, if each value of the variable is divided by `(-3)` , then the standard deviation of the new set of 50 values of x will be

Options

A. 15
B. `-5`
C. 5
D. `-15`

Answer

To find the standard deviation of the new set of values after dividing each value of the variable \( x \) by \(-3\), we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Given Data**:
- The standard deviation of the original set of values \( x \) is given as \( \sigma = 15 \).
- The number of values \( n = 50 \).

2. **Understand the Effect of Division on Standard Deviation**:
- When each value in a dataset is multiplied or divided by a constant \( a \), the standard deviation of the new dataset is given by:
\[ \sigma' = |a| \cdot \sigma \]
- Here, \( a = -\frac{1}{3} \) since we are dividing by \(-3\).

3. **Calculate the Absolute Value of \( a \)**:
- The absolute value of \( a \) is:
\[ |a| = \left| -\frac{1}{3} \right| = \frac{1}{3} \]

4. **Substitute the Values into the Formula**:
- Now, substitute \( |a| \) and the original standard deviation \( \sigma \) into the formula:
\[ \sigma' = |a| \cdot \sigma = \frac{1}{3} \cdot 15 \]

5. **Perform the Calculation**:
- Calculate \( \sigma' \):
\[ \sigma' = \frac{15}{3} = 5 \]

6. **Conclusion**:
- The standard deviation of the new set of values after dividing each value by \(-3\) is \( 5 \).

### Final Answer:
The standard deviation of the new set of 50 values of \( x \) will be \( 5 \).

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