Question

If the mean of the following data is 20.6. Find the value of p.
x:
10
15
p
25
35
f:
3
10
25
7
5

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 = 530 + 25p , Σfi = 50

MEAN = Σfixi / Σfi  

Given : Mean = 20.6  

20.6  = 530 + 25p /50  

20.6 × 50 = 530 + 25p

1030 = 530 + 25p

25 p = 1030 - 530

25p = 500

p = 500/25 = 20

p = 20  

Hence, the value of ‘p’ is 20  .

HOPE THIS ANSWER WILL HELP YOU…

Answer 2

Answer :

The value of p is 20.

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 -

$\begin{tabular}{| c | c | c |}\cline{1-3}x_{i} & f_{i} & f_{i}x_{i} \\ \cline{1-3}10 & 3 & 30 \\\cline{1-3}15 & 10 & 150 \\ \cline{1-3}p & 25 & 25p \\ \cline{1-3}25 & 7 & 175 \\ \cline{1-3}35 & 5 & 175 \\ \cline{1-3} & \Sigma f_{i}=50 & \Sigma f_{i}x_{i}=530+25p \\ \cline{1-3}\end{tabular}$

Since, mean -

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

$\implies Mean=20.6$

$\implies 20.6=530+\frac{25p}{50}$

$\implies 20.6\times 50 =530+25p$

$\implies 1030=530+25p$

$\implies 25p=1030-530$

$\implies 25p=500$

$\implies p=20$