Grades 11-12 Video Solutions 2022-2022_11-12

Video Transcription

Five numbers have a mean of 24 the mean of the three smallest numbers is 9 and the mean of the three largest numbers is 28 what is the median of the five numbers?  Let's call these numbers x1 x2 x3 x4 and x5 and just order them like this  So we want to calculate x3 which is their median So rewriting the information that we know we know that the mean of all five of the numbers is 24  the mean of the lowest three is 19 and the mean of the biggest three is 28 and  So now let's add up these two equations  To get x1 plus x2 plus 2 x3 because it's counted in both Plus x4 plus x5 all divided by 3 is 47  But now interestingly enough This contains an x1 x2 x3 x4 and x5 and we know that their sum is equal to 24 times 5  So I'm going to replace them with the 24 times 5 and then keep the remaining x3 that we have  Well, we know that 24 divided by 3 is 8 and 8 times 5 is 40 So if I subtract 40 from both sides, I get that x3 over 3 is 7  Multiplying by 3 gets us that x3 is 21. So our final answer is 21

Video Summary

The problem involves determining the median of five numbers given specific mean conditions. The mean of all five numbers is 24, and the mean of the three smallest numbers is 9, while the mean of the three largest numbers is 28. By setting equations based on these conditions and manipulating the sums and differences of equations, the value of the third number, which represents the median when the numbers are ordered, is found to be 21. Thus, the median of the five numbers is 21.

Keywords

median

mean conditions

five numbers

equations

value determination