Question

If the mean of the following data is 18.75. Find the value of p.
xi:
10
15
p
25
30
fi:
5
10
7
8
2

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 = 460 + 7p  ,Σfi = 32

MEAN = Σfixi / Σfi  

Given : Mean = 18.75

18.75 = (460 + 7p) / 32

18.75 × 32 =  (460 + 7p)

600 =  (460 + 7p)

7p = 600 - 460  

7p = 140

p = 140/7  

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 -

$\begin{tabular}{| c | c | c |}\cline{1-3}x_{i} & f_{i} & f_{i}x_{i} \\ \cline{1-3}10 & 5 & 50 \\ \cline{1-3}15 & 10 & 150 \\ \cline{1-3}p & 7 & 7p \\ \cline{1-3}25 & 8 & 200 \\ \cline{1-3}30 & 2 &60 \\ \cline{1-3} & \Sigma f_{i}=32 & \Sigma f_{i}x_{i}=460+7p \\ \cline{1-3}\end{tabular}$

Since, mean -

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

$\implies Mean=18.75$

$\implies 18.75=\frac{(460+7p)}{32}$

$\implies 18.75\times 32=460+7p$

$\implies 600=460+7p$

$\implies 7p=600-460$

$\implies 7p=140$

$\implies p=20$