Study Means Data

Introduction

       The term "means data" is one of the frequently used word in statistics. The means data are formed from the set of a sequence of data. In the statistical meaning of word "Means data" is used to find out the "average data" of a group of data values. The mathematical representations of the term "means data"  are the "average data" of  a series of numbers. Let us study mean data and solve some sample problems on means data.

 

Definition for Study Means Data:

 

      The mean data of a series of N experiments, Yl, Y2, Y3, Y4, ..., YN  is equal  as the determinant of total experiments divided by the total number of experiments, N. Mathematics notation of  mean data as,                              

                   Mean = ( `1/n``sum_(i =1)^n` x i                           

where
                 n  =  the number of values (data).
                x1 =  the 1st data point, x2 = the 2nd data point, .... xi = the ith data point.
                xi  =   ith data point, x1 = the 1st data point, x2 = the 2nd data point, etc.
  The symbol Sigma ( `sum` ) is used to show summation, and i = 1 to n indicates that the values of xi from i = n are added.
  The sum is divided by  number of terms added, n.

 

Examples for Study Mean Data:

 

Example 1:
    Calculate the means data of the given series:
               7, 3, 9, 0, 4, 1
Solution:

             Mean = (`1/n` ) `sum_(i=1)^n` xi     =   (`1/ 6` ) `sum_(i=1)^6` xi

            where

                       n = Total number of data = 6.

                      x1 = 7, x2 = 3, x3 = 9, x4 = 0, x5 = 4, x6 = 1

           Substituting

           Means data = `(7 + 3 + 9 + 0 + 4 + 1) / 6`   = `24 / 6`   = 4.

                    4 is the means of data.

 

Example 2 :

    Calculate the means data of unordered temperature(T) readings,
                        123, 366, 101, 444, 101, 366, 123, 366, 366, 101, 366,101.
Solution:

         Ordered series are,

                       101, 101, 101, 101, 123, 123, 366, 366, 366, 366, 366, 444.

        Determine frequency(f) of every reading

        Frequency Distribution(f)(xi) Table:

           T(temp)      
   Frequency - (f)     
                (f)(xi) = temp x f
101 4 404
123 2 246
366 5 1830
444 1 444
  12 2924

                                        

Then the calculate the means data,

                          Means Data  = ( `1/n` ) `sum_(i=1)^n` xi

                                           xi = 4(101) + 2(123) + 5(366) + 1(444)

                                           n = 12

                          Mean Data    =  `(2924) / 12 `    =   243.7

       Now you can get some ideas about study mean data.