Sunday, 4 December 2011

Arithmetic Mean (ungroup data & group data)

Defination:

       Arithmetic mean can be defined as: 
       The sum of all values in the series divided by the total numbers of values in the series.

The method of Arithmetic mean is also known as:
-                     Arithmetic mean
-                     Mean
-                     Simple mean
-                     Average
-                     Mean by direct method

Arithmetic Mean (ungroup-data)

Formula:
 Mean = sum of elements / number of elements
               = a1+a2+a3+.....+an/n
Arithmetic Mean  = ΣX/n
 where
               X = Individual value
               n = Total number of values


   Example: To find the mean of 3,5,7.

       Step 1:      Find the sum of the numbers.
                         3+5+7 = 15

       Step 2:      Calculate the total number.
                         there are 3 numbers.

       Step 3:      Finding mean.
                        15/3 = 5                       Ans = 5

Arithmetic Mean (group-data) :

Formula:
Arithmetic Mean  = ΣfX/Σf
 where
               X = Individual value
               f = Frequency




Grouped Data Arithmetic Mean Example:.

X -Value          Frequency(f)                 ΣfX
1                      2                                  1 * 2 = 2
2                      3                                  2 * 3 = 6
3                      2                                  3 * 2 = 6
                        Σf = 7                           ΣfX= 14


   Step 1:          Find Σf.
                         Σf = 7

   Step 2:          Now, find ΣfX.
                         ΣfX = 14

   Step 3: Now, Substitute in the above formula given
             Arithmetic mean = ΣfX/Σf = 14/7 = 2


Example:.

Classes Frequency      
of Class           
Age (years)      f                    
0  --- 5             6                   
5  --- 10           12                 
10 ---15           19                 
15 ---20           3                   
Total                                      
Find Arithmetic mean for given data.

As the formula for  A.M (Group data) = ΣfX/Σf

So we need  “X” first

Classes Frequency    Mid Point
of Class           
Age (years)      f                      X                    fX
0  --- 5             6                    2.5                   15
5  --- 10           12                  7.5                   90
10 ---15           19                  12.5                 237.5
15 ---20           3                    17.5                 52.5
Total               40                                           395

Note:    [In this example we have already class boundary, If  class boundary not given to find A.M then no problem and we will not make class boundary. Class boundary is required only for  Median, Mode, Quartile, Decile, Percentile

1 comment: