Question

Find the mean value of the following data:
x:
19
21
23
25
27
29
31
f:
13
15
16
18
16
15
13

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 = 2650 , Σfi = 106

MEAN = Σfixi / Σfi  

MEAN = 2650/106 = 25  

MEAN = 25  

Hence, the MEAN value  is 25 .

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

From the picture, it is absolutely clear that the sum of the quantities in the column ( $\bold{f_{1}x_{1}}$ ).

Hence, sum of the column( $\bold{f_{1}x_{1}}$ ) = 2650

And, we know that arithmetic mean is the sum of the given quantities by the total number of the quantities.

Hence from the picture it is clear that, the total number of quantities = 106

Now,

Arithmetic mean = Sum of given quantities / Total number of quantities

Arithmetic mean = 2650 / 106

After performing simple division we get,

Arithmetic mean = 25