Problem Solving

$10, $11, $11, $12, $12, $14, $16, $17, $21, $22

The various prices that a certain product were sold for at retailers in City X is shown above. How many prices were greater than the median price but less than the mean price?

(A) None
(B) One
(C) Two
(D) Three
(E) Four

The OA is B.

Can any expert explain this PS question, please? I don't have it clear. Thanks.

Hello LUANDATO.

Let's take a look at your question.

The median price of the set consist in sum the two numbers in the middle of the set (12 and 14) and then divide the result by 2. In our case, the median price is $$\frac{12+14}{2}=\frac{26}{2}=13.$$

By the other hand, the mean price is the sum of all the numbers and then divide by the total of numbers in the set. In our case, the mean price is $$\frac{10+11+11+12+12+14+16+17+21+22}{10}=\frac{146}{10}=14,6.$$

Now, the only number on the list that satisfy the condition is 14.

So, there is only ONE number such that it is greater than the median price but less than the mean price.

That is why the correct option is B.

I hope this clarify it to you.

I'm available if you'd like any follow up.