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Example The mean of a certain number of observations is 40. If two or more items with values 50 and 64 are added to this data, the mean rises to 42. Find the number of items in the original data.

Solution:

Let 'n' be the number of observations whose mean = 40.

total of n values.

Two more items of values 50 and 64 are added therefore, total of (n + 2) values :


Now new mean is 42.

\ New

\

\ 42n + 84 = 40n + 114

\ 2n = 30

\ n = 15

Therefore, the number of items in the original data = 15.


Example The sum of deviations of a certain numbers of observations measured from 4 is 72 and the sum of deviations of observations measured from 7 is -3. Find the number of observations and their mean.

Solution:

Let 'n' be the required number of observations , therefore,

......Note and therefore,

Subtracting the two equations we get,



(-)     (+)     (+)


            3n=75
\          n = 25

Putting n = 25 in , we get

     
     
     

Now Mean is given by

 

Index

4.1 Introduction
4.2 Arithmetic Mean
4.3 Properties of Arithmetic Mean
4.4 Median
4.5 Mode
4.6 Empirical relation between mean, median & mode

Chapter 5





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