Question

The least and greatest numbers in a list of $7$ real numbers are $2$ and $20$ respectively. The median of the list is $6$ and the number $3$ occurs most often in the list. Which of the following could be the average (arithmetic mean) of the numbers in the list?
I. 7
II. 8.5
III. 10

• A. I only
• B. I and II only
• C. I and III only
• D. II and III only
• E. I, II, and III

Answer 1

The correct option is E I, II, and III

So, we have here the list is composed of $2,3,3,6,x,y,20$.

Here we try choose the least values for $x,y$ respectively.

So lets get least values for $x,y=6,7$ respectively.

Least $=$ $\frac{2+3+3+6+7+8+20}{7}=7$;

We choose for the most 1$8.5$ and $19.5$.

Most $=$ $\frac{2+3+3+6+18.5+19.5+20}{7}$ $=$ Approximately $10$

I just chooses $18.5$ and $19.5$ to show it would work even with real values, but just more ranges for smallest and biggest numbers.

So, the answer is E.