The frequency of occurrence of $8$ symbols $(a-h)$ is shown in the table below. A symbol is chosen and it is determined by asking a series of $\text{"yes/no"}$ questions which are assumed to be truthfully answered. The average number of questions when asked in the most efficient sequence, to determine the chosen symbol, is _______________ (rounded off to two decimal places).
| Symbols |
a |
b |
c |
d |
e |
f |
g |
h |
| Frequency of occurence |
$\frac{1}{2}$ |
$\frac{1}{4}$ |
$\frac{1}{8}$ |
$\frac{1}{16}$ |
$\frac{1}{32}$ |
$\frac{1}{64}$ |
$\frac{1}{128}$ |
$\frac{1}{128}$ |