Question

the mean of 35 observations. is 20 if the mean of the 18 observations is 15

Answer 1

Solution:

Given:The mean of 35 observations is 20.The mean of first 18 observation is 15.
the mean of last 18 observations is 25.
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To find: 18th observation.
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mean= sum of the numbers / total number of observations

let the total of 35 observations be x, (1 st term to 35 th term )
then,

mean of 35 observations =x/35
                                       20 =x/35
                                20(35) =x
                                         x =700..(i)
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let the sum of first 18 observations be y (1st term to 18 th term)
 
mean of first 18 observations = y/18
                                       25(18) =y
                                                 y =450..(ii)
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let the sum of last  18 observations be z, (18th term to 35 term)

mean of last 18 observations = z/18
                                       15(18) = z
                                                 z = 270..(iii)
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if we add y and z it would be equal to,

=(1 st term to 18 th term)+(18 th term to 35 th term)
=(1st term to 35 th term) + (18th term)          (as,18th term is repeated in y and z)

let 18th term be a,
then,
x+a=y+z
700+a=450+270
         a=720-700
         a=20

∴The 18 th term is 20.

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                                   Hope it Helps.