Mathematics

The key is recognizing that variance measures how spread out data is from the mean—and you can express it as a formula using the frequencies. First, find the mean in terms of the unknown frequency $f$, then use the variance formula $\sigma^2 = \frac{\sum f_i(x_i - \bar{x})^2}{\sum f_i}$ and set it equal to 16. This gives you an equation in $f$ that you can solve.

The key is recognizing that variance measures how spread out data is from the mean—and you can express it as a formula using the frequencies. First, find the mean in terms of the unknown frequency $f$, then use the variance formula $\sigma^2 = \frac{\sum f_i(x_i - \bar{x})^2}{\sum f_i}$ and set it equal to 16. This gives you an equation in $f$ that you can solve.