Find the mean and variance of the frequency distribution given below:
$\begin{array}{|l|l|l|l|l|} \hline x & 1 \leq x < 3 & 3 \leq x < 5 & 5 \leq x < 7 & 7 \leq x < 10 \\ \hline f & 6 & 4 & 5 & 1 \\ \hline \end{array}$

(N/A) To find the mean and variance,we first determine the class marks $(x_i)$ for each interval:
$\begin{array}{|c|c|c|c|c|} \hline \text{Class} & f_i & x_i & f_i x_i & f_i x_i^2 \\ \hline 1-3 & 6 & 2 & 12 & 24 \\ \hline 3-5 & 4 & 4 & 16 & 64 \\ \hline 5-7 & 5 & 6 & 30 & 180 \\ \hline 7-10 & 1 & 8.5 & 8.5 & 72.25 \\ \hline \text{Total} & N=16 & & \Sigma f_i x_i = 66.5 & \Sigma f_i x_i^2 = 340.25 \\ \hline \end{array}$
$\text{Mean } (\bar{x}) = \frac{\Sigma f_i x_i}{N} = \frac{66.5}{16} = 4.15625 \approx 4.16$
$\text{Variance } (\sigma^2) = \frac{\Sigma f_i x_i^2}{N} - (\bar{x})^2 = \frac{340.25}{16} - (4.15625)^2$
$\sigma^2 = 21.265625 - 17.274414 = 3.991211 \approx 3.99$