Question

A sample consisting of five observations has an arithmetic mean of 12 and a median of 14. What is the smallest value that the range (largest observation minus smallest) can assume for such a sample?

Answer 1

5

Explanation:

This is Given:

Median=14

Mean=12

Since the median is 14, to get the minimum range, we keep the numbers after the median as small as can be.

So our numbers are:

y,x,14,14,14

The first number must be as large as possible.

So:

Let x stand for the number

Cross multiply

2x+42=5*12

2x=60-42

2x=18

Divide both sides by 2

x=9.

Therefore, the five observations are:

9,9,14,14,14

So, the smallest range

=14-9

=5

Answer 2

5

Explanation:

In the sample:

Median=14

Mean=12

Since the median is 14, to get the minimum range, we keep the values after the median as small as possible.

Therefore our numbers are:

*,*,14,14,14

The first number must be as large as possible.

Therefore:

Let x be the number

`Mean=(x+x+14+14+14)/(5)=12\\(2x+42)/(5)=12`

CrisCros multiply

2x+42=5*12

2x=60-42

2x=18

Divide both sides by 2

x=9.

Therefore, the five observations are:

9,9,14,14,14

Therefore, the smallest range

=14-9

=5