Question

Find the mean of each of the following frequency distributions :
Class interval:
0−8
8−16
16−24
24−32
32−40
Frequency:
5
6
4
3
2

Answer 1

STEP DEVIATION METHOD:

Step deviation method is used in the cases where the deviation from the assumed mean 'A' are multiples of a common number. If the values of ‘di’ for each class is a multiple of ‘h’ the calculation become simpler by taking ui= di/h = (xi - A )/h

Here, h is the class size of each class interval.

★★ Find the class marks of class interval. These class marks would serve as the representative of whole class and are represented by xi.  

★★ Class marks (xi)  = ( lower limit + upper limit) /2

★★ We may take Assumed mean 'A’ to be that xi which lies in the middle of x1 ,x2 …..xn

MEAN = A + h ×(Σfiui /Σfi) , where ui =  (xi - A )/h

[‘Σ’ Sigma means ‘summation’ ]

FREQUENCY DISTRIBUTION TABLE IS IN THE ATTACHMENT  

From the table : Σfiui = -9 , Σfi = 20

Let the assumed mean, A = 20,  h = 8

MEAN = A + h ×(Σfiui /Σfi)

MEAN = 20  + 8(-9/20)

= 20 -  72/20

= 20 - 18/5

= 20 - 3.6

= 16.4

Mean = 16.4

Hence, the mean is 16.4

HOPE THIS ANSWER WILL HELP YOU….

Answer 2

Solution: To find the mean of the following observations
let us first complete the table

$\begin{table}[] \begin{tabular}{llll} Class & Freq & Class Mark & xifi \\ 0-8 & 5 & \:\:4 & 20 \\ 8-16 & 6 & \:\:12 & 72 \\ 16-24 & 4 & \:\:20 & 80 \\ 24-32 & 3 & \:\:28 & 84 \\ 32-40 & 2 & \:\:36 & 72 \\ &\Sigma=20 & &\Sigma=328 \end{tabular} \end{table}$

We know that, formula for Direct method:

$\bar x=\frac{\Sigma x_{i}f_{i}}{\Sigma f_{i}}\\\\\bar x=\frac{40+72+80+84+72}{20}\\\\\bar x=\frac{328}{20}\\\\\bar x=16.4$

Hope it helps you.