The standard deviation of some temperature data in `.^(@)C` is 5 .If the data were converted into `.^(@)F` then variance would be

Options

A. 81
B. 57
C. 36
D. 25

Explanation

To solve the problem, we need to find the variance of temperature data in Fahrenheit given that the standard deviation in Celsius is 5.

### Step-by-step Solution:

1. **Understand the relationship between Celsius and Fahrenheit:**
The formula to convert Celsius (C) to Fahrenheit (F) is:
\[ F = \frac{9}{5}C + 32 \]
This formula consists of a multiplication factor (\(\frac{9}{5}\)) and a constant addition (32).

2. **Identify the effect of constants on standard deviation:**
When converting data using a linear transformation of the form \(kX + b\), where \(k\) is a constant and \(b\) is a constant added to the data:
- The standard deviation is affected only by the multiplication factor \(k\).
- The addition of a constant \(b\) does not affect the standard deviation.

3. **Calculate the standard deviation in Fahrenheit:**
Given that the standard deviation in Celsius is 5, we can find the standard deviation in Fahrenheit using the multiplication factor:
\[ \text{Standard deviation in Fahrenheit} = \frac{9}{5} \times \text{Standard deviation in Celsius} \]
Substituting the known value:
\[ \text{Standard deviation in Fahrenheit} = \frac{9}{5} \times 5 \]
Simplifying this gives:
\[ \text{Standard deviation in Fahrenheit} = 9 \]

4. **Calculate the variance in Fahrenheit:**
Variance is the square of the standard deviation. Therefore, we can find the variance in Fahrenheit as follows:
\[ \text{Variance in Fahrenheit} = (\text{Standard deviation in Fahrenheit})^2 \]
Substituting the value we found:
\[ \text{Variance in Fahrenheit} = 9^2 = 81 \]

### Final Answer:
The variance of the temperature data in Fahrenheit is **81**.