Question

A list of measurements in increasing order is 4, 5, 6, 8, 10, and x. if the median of these measurements is \small \frac{6}{7} times their arithmetic mean, what is the value of x ?

Answer 1

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