Acertain list consists of 3 different numbers. does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers? (1) the range of the 3 numbers is equal to twice the difference between the greatest number and the median.(2) the sum of the 3 numbers is equal to 3 times one of the numbers.

Answer with explanation:

A certain list consists of 3 different numbers.

Does the median of the 3 numbers equal the average (arithmetic mean) of the 3 numbers?

Let the three numbers be x, y, and z, where x < y < z.

Now, the median will be y and the average will be

We have to tell if or

(1) The range of the 3 numbers is equal to twice the difference between the greatest number and the median.

Range is the largest number minus the smallest number of the set,

Here range =  z - x.

We are given in the statement that

Solving this we get;

or

So, this condition is fulfilled.

(2) The sum of the 3 numbers is equal to 3 times one of the numbers.

The sum of 3 numbers cannot be equal to 3 times the smallest number or 3 times largest number as the given numbers are distinct and they cannot be equal to mean. So, median = mean.

or

So, this condition is fulfilled.

a

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