The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency 'f' using assumed mean method

$\begin{matrix} Pocket allowance & Number of children 11 - 13 & 7 13 - 15 & 6 15 - 17 & 9 17 - 19 & 13 19 - 21 & f 21 - 23 & 5 23 - 25 & 4 \end{matrix}$

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C 20
Let the assumed mean 'a' be 18

$\begin{matrix} C l a s s I n t e r v a l & f_{i} & x_{i} & d_{i} = x_{i} - a & f_{i} d_{i} 11 - 13 & 7 & 12 & - 6 & - 42 13 - 15 & 6 & 14 & - 4 & - 24 15 - 17 & 9 & 16 & - 2 & - 18 17 - 19 & 13 & 18 = a & 0 & 0 19 - 21 & f & 20 & 2 & 2 f 21 - 23 & 5 & 22 & 4 & 20 23 - 25 & 4 & 24 & 6 & 24 \end{matrix}$

Here,

$\sum f_{i} = 44 + f$

$\sum f_{i} d_{i} = 2 f - 40$

$∵ M e a n = a + \frac{\sum f_{i} d_{i}}{\sum f_{i}}$

$\Rightarrow 18 = 18 + \frac{2 f - 40}{44 + f} \Rightarrow 2 f - 40 = 0 \Rightarrow f = 20$

$∴$ The missing frequency is 20.

Suggest Corrections

Similar questions

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency f.

$\begin{matrix} Daily pocket allowance (in Rs) & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 & 19 - 21 & 21 - 23 & 23 - 25 Number of workers & 7 & 6 & 9 & 13 & f & 5 & 4 \end{matrix}$

Q. The following distribution shows the daily pocket allowance of children of a locality . The mean pocket allowance is

R s . 18.

Find the missing frequency

f

Dally pocket allowance (in Rs)	$11 - 13$	$13 - 15$	$15 - 17$	$17 - 19$	$19 - 21$	$21 - 23$	$23 - 25$
Number of children	$7$	$6$	$9$	$13$	$f$	$5$	$4$

The following distribution shows the daily pocket allowance of children of a locality. If the mean pocket allowance is Rs. 18, find the missing frequency f.
$\begin{matrix} Daily pocket allowance(in Rs) & 11 - 13 & 13 - 15 & 15 - 17 & 17 - 19 & 19 - 21 & 21 - 23 & 23 - 25 Frequency & 7 & 6 & 9 & 13 & f & 5 & 4 \end{matrix}$

Join BYJU'S Learning Program

The following distribution shows the daily pocket allowance of children of a locality. The mean pocket allowance is Rs.18. Find the missing frequency 'f' using assumed mean method Pocket allowanceNumber of children11−13713−15615−17917−191319−21f21−23523−254