Given:
(i) The measurements of the data in increasing order are 4,5,6,8,10 and X
(ii) Total number of observations (n) = 6 which is even
(iii) Median = (6 / 7)× Arithmetic Mean
Concept: If there are even number of observations then the median can be calculated as
Median = [(n /2)the term + {(n/2)+1} term] / 2
Here, n = 6,
Median = [(6 /2)the term + {(6/2)+1} term] / 2 = [ 3rd term + 4th term] /2
Median = [ 6 + 8] /2 = 7
Arithmetic Mean (AM) = Sum of the observation / Number of observations
or, = [ 4 + 5 + 6 + 8 + 10 + X] / 6
or, = [33 + X] / 6
According to the problem,
Median = (6 / 7)× AM
or, 7 = ( 6 / 7 ) × ( 33 + X) /6
or, 49 = 33 + X
or, X = 16
Hence, the value of X will 16
