Which one of the following is correct?

Calculation:

Given,

The sum and sum of squares of the observations corresponding to length X in cm and weight Y in gm of 50 tropical tubers are given as:
\(\Sigma X\) = 200, \(\Sigma Y\) = 250, \(\Sigma X^2\)= 900, \(\Sigma Y^2\) = 1400 

The formula for variance is:

\( \text{Variance} = \frac{\Sigma X^2}{N} - \left( \frac{\Sigma X}{N} \right)^2 \)

Where N = 50 is the number of observations.

Variance of X:

\( \text{Variance of } X = \frac{\Sigma X^2}{N} - \left( \frac{\Sigma X}{N} \right)^2 \)

Substituting the given values:

\( \text{Variance of } X = \frac{900}{50} - \left( \frac{200}{50} \right)^2 \)

\( \text{Variance of } X = 18 - 16 = 2 \)

Variance of Y:

\( \text{Variance of } Y = \frac{\Sigma Y^2}{N} - \left( \frac{\Sigma Y}{N} \right)^2 \)

Substituting the given values:

\( \text{Variance of } Y = \frac{1400}{50} - \left( \frac{250}{50} \right)^2 \)

\( \text{Variance of } Y = 28 - 25 = 3 \)

Conclusion:

\( \text{Variance of } X < \text{Variance of } Y \)

Hence, the correct answer is Option 2.