Question

Calculate the mean value of the following distribution:
x:
5
6
7
8
9
f:
4
8
14
11
3

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 = 281 , Σfi = 40

MEAN = Σfixi / Σfi  

MEAN = 281/40 = 7.025  

MEAN = 7.025  

Hence, the MEAN value is 7.025 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Answer :

The mean is 7.025 .

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 -

$\begin{tabular}{| c | c | c |}\cline{1-3}x_{i} & f_{i} & f_{i}x_{i} \\ \cline{1-3}5 & 4 & 20 \\ \cline{1-3}6 & 8 & 48 \\ \cline{1-3}7 & 14 & 98 \\ \cline{1-3}8 & 11 & 88 \\ \cline{1-3}9 & 3 & 27 \\ \cline{1-3} & \Sigma f_{i}=40 & \Sigma f_{i}x_{i}=281 \\ \cline{1-3}\end{tabular}$

Since, mean -

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

$\implies \frac{281}{40}$

$\implies 7.025$