Find the missing frequency '$f$' in the following table, if the mean of the given data is 18. Hence find the mode.

| Daily Allowance | Number of Children |
|-----------------|--------------------|
|

Question

Find the missing frequency '$f$' in the following table, if the mean of the given data is 18. Hence find the mode.

| Daily Allowance | Number of Children |
|-----------------|--------------------|
| $11 - 13$ | $7$ |
| $13 - 15$ | $6$ |
| $15 - 17$ | $9$ |
| $17 - 19$ | $13$ |
| $19 - 21$ | $f$ |
| $21 - 23$ | $5$ |
| $23 - 25$ | $4$ |

Accepted Answer

Step 1: Constructing the table with class marks $x_i$: $12, 14, 16, 18, 20, 22, 24$ and $f_i$: $7, 6, 9, 13, f, 5, 4$. $\sum f_i = 44 + f$ and $\sum f_i x_i = 752 + 20f$.
Step 2: Mean $= \frac{\sum f_i x_i}{\sum f_i} = \frac{752 + 20f}{44 + f} = 18$
Step 3: $752 + 20f = 18(44 + f) = 792 + 18f \Rightarrow 2f = 40 \Rightarrow f = 20$
Step 4: Modal class is $19 - 21$ (highest frequency $= 20$). Mode $= 19 + \frac{20 - 13}{2(20) - 13 - 5} 	imes 2 = 19 + \frac{7}{22} 	imes 2 = 19 + \frac{14}{22} = 19 + \frac{7}{11}$
Step 5: $\approx 19.64$

Question

Solution