Question

For a particular list of four distinct integers the mean, median and range have the same value. If the least integer in the list is 10, what is the greatest value for an integer in the list?

Answer 1

The greatest value = 30

Explanation:

Let the greatest value in the given 4 integers be x.

So, the least integer is 10 and the greatest integer is x.

Let the remaining two integers be 'a' and 'b'.

Now,

Mean =
`(10+a+b+x)/(4)`

Median = Average of 2nd and 3rd observations

=
`(a+b)/(2)`

Range = x - 10

From the given information,

Mean = Median = Range

Therefore,

`(10+a+b+x)/(4) =(a+b)/(2) =x - 10`

From the first two ratios,

10 + a + b + x = 2a + 2b

or,

a + b = 10 + x --- (1)

From the last two ratios,

a + b = 2x - 20 --- (2)

From (1) and (2),

10 + x = 2x - 20

10 + 20 = 2x - x

x = 30

Hence, the greatest value = 30