Calculate the variance and the standard deviation of the following classified data. 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 9.0, 9.1, 9.2, with their respective frequencies of 2, 6, 8, 1, 17, 17, 24, 18, 13, 10, 4,

This is not the appropriate board to post this. Here is for biology.

Your question should have been in the math-sciences section:
https://www.askmehelpdesk.com/math-sciences/

Anyway, the formula for variance is

\sigma = \sqrt{\frac{\Sigma(x-\bar{x})}{n}}

Where \sigma is the standard deviation and squaring it, you have the variance.