Loading....
Coupon Accepted Successfully!

 

Mean of Grouped Data

If n observations in the raw data consists of n distinct values denoted by x1, x2, x3, …, xn of the observed variable x occurring with frequencies f1, f2, …, fn respectively, then the arithmetic mean of the variate x is given by x, where

                                      

                                          =

                                       

         where N = 

 
Example

Find the mean of the following data

x: 19 21 23 25 27 29 31
f: 13 15 16 18 16 15 13
 

 

Solution
xi fi xifi
19 13 247
21 15 315
23 16 368
25 18 450
27 16 432
29 15 435
31 13 403
Total N = Σfi = 106 Σxifi = 2650


We know that  xifi =  × 2650 = 25.

 
 
Example

The marks of 41 students of Xth class are given in the table. Five the mean marks secured by one student.

Marks: 20 15 17 30 22 25
Frequency: 10 2 5 4 12 8
 

 

Solution
Marks (xi) Frequency (fi) xifi
20 10 200
15 2 30
17 5 85
30 4 120
22 12 264
25 8 200

Total

N = Σfi 41

Σxifi = 899

                  = 21.93.

 

 

Example

In the first proof reading of a book containing 800 pages, the following distribution of misprints were obtained.

No. of Misprints per page

No. of Pages

0

654
1 95
2 36
3 9
4 5
5 1

Total

800

Find the average number of misprints per page.
 

Solution

No. of misprints Per page (xi)

No. of pages
(fi)

fi xi

0 654 00
1 95 95
2 36 72
3 9 27
4 5 20
5 1 5
  N = Σfi = 800 Σfixi = 219

 =  = 0.27375
Hence the average number of misprints per page = 0.27375.

 





Test Your Skills Now!
Take a Quiz now
Reviewer Name