Step 1: Find the Class Marks ($x_i$) and Calculate $f_i x_i$ We calculate the mid-point ($x_i$) for each class interval using the formula $x_i = \frac{\text{Lower Limit} + \text{Upper Limit}}{2}$ and then multiply by the frequency ($f_i$).

Daily pocket allowance	Number of children ($f_i$)	Class Mark ($x_i$)	$f_i x_i$
11 - 13	7	12	84
13 - 15	6	14	84
15 - 17	9	16	144
17 - 19	13	18	234
19 - 21	$f$	20	$20f$
21 - 23	5	22	110
23 - 25	4	24	96

Step 2: Calculate Total Frequency ($\sum f_i$) and Total Sum ($\sum f_i x_i$) Total Frequency ($\sum f_i$) = $7 + 6 + 9 + 13 + f + 5 + 4 = 44 + f$.

Total Sum ($\sum f_i x_i$) = $84 + 84 + 144 + 234 + 20f + 110 + 96 = 752 + 20f$.

Step 3: Apply the Mean Formula Mean = $\frac{\sum f_i x_i}{\sum f_i}$. Given Mean = 18. Substituting the values, we get:

$$18 = \frac{752 + 20f}{44 + f}$$

Step 4: Solve for $f$

$$18(44 + f) = 752 + 20f$$ $$792 + 18f = 752 + 20f$$ $$792 - 752 = 20f - 18f$$ $$40 = 2f$$

$f = 20$.

Thus, the missing frequency is 20.