Question

Find the missing frequency (p) for the following distribution whose mean is 7.68.
x:
3
5
7
9
11
13
f:
6
8
15
p
8
4

Answer 1

ARITHMETIC MEAN OR MEAN OR AVERAGE :  

The arithmetic mean of a set of observations is obtained by dividing the sum of the values of all observations by the total number of observations .

Mean = Sum of all the observations / Total number of observations .

MEAN = Σfixi / Σfi

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfixi = 303 + 9p , Σfi = 41 + p  

MEAN = Σfixi / Σfi  

Given : Mean = 7.68  

7.68   = (303 + 9p) / 41 + p  

7.68 ×(41 + p )  =  (303 + 9p)  

314.88 + 7.68 p = (303 + 9p)  

(303 + 9p) = 314.88 + 7.68 p  

9p - 7.68 p = 314.88 - 303

1.32p = 11.88

p = 11.88/1.32 = 1188/132 = 9

p = 9

Hence, the value of ‘p’ is 9.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

$\large\bf\implies\: mean\:=\:7.68$

$\large\sf\implies\frac{\:9p\:+303}{\:p\:+\:41}\:=\:7.68$

$\large\sf\implies\:9p\:+303\:=\:7.68(p+41)$

$\large\sf\implies\:1.32p\:=11.88$

$\large\bf\implies\:p\:=\:9$