Question

Find the value of p for the following distribution whose mean is 16.6.
x:
8
12
15
p
20
25
30
f:
12
16
20
24
16
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 = 1228 + 24p , Σfi = 100

MEAN = Σfixi / Σfi  

Given : Mean = 16.6

16.6   = (1228 + 24p) / 100

16.6 × 100 =  (1228 + 24p)  

1660 = 1228 + 24p

24p = 1660 - 1228

24p = 432

p = 432/24 = 18

p = 18

Hence, the value of ‘p’ is 18.

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The value of p is 18.

Step-by-step explanation :

Arithmetic Mean -

Mean of a set of observations is obtained by dividing the sum of all observations by the total number of observations .

Mean = Sum of all observations / Total observations .

$Mean=\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

where $\Sigma$ means summation.

Frequency Distribution Table -

$\begin{tabular}{| c | c | c |}\cline{1-3}x_{i} & f _{i} & f_{i}x_{i} \\ \cline{1-3}8 & 12 & 96 \\ \cline{1-3}12 & 16 & 192 \\ \cline{1-3}15 & 20 & 300 \\ \cline{1-3}p & 24 & 24p \\ \cline{1-3}20 & 16 & 320 \\ \cline{1-3}25 & 8 & 200 \\ \cline{1-3}30 & 4 & 120 \\ \cline{1-3}& \Sigma f_{i}=100 & \Sigma f_{i}x_i}=1228+24p \\ \cline{1-3} \end{tabular}$

Since, mean -

$\implies\frac{\Sigma f_{i}x_{i}}{\Sigma f_{i}}$

$\implies Mean=16.6$

$\implies 16.6=\frac{1228+24p}{100}$

$\implies 16.6\times 100=1228+24p$

$\implies 1660=1228+24p$

$\implies 24p=1660-1228$

$\implies 24p=432$

$\implies p=\frac{432}{24}$

$\implies p=18$