# Finding x and y in stem-and-leaf diagram

#### lecloc

Hello! I've just recently came across this website due to my difficulties in solving Math questions. I'm really not good with Math but I am willing to learn and solve questions on my own, especially now that my exams are in 5 months time.

Anyway, here is one of the questions on the practice paper that I'm currently struggling with:

The weights of the 20 students are shown in the following diagram (in kg). The median weight is 67kg.

Stem (Tens) Leaf (Units)
5 3 4 6 8 9
6 1 2 4 6 6 y
7 2 4 6 7 8
8 3 x 3 9

Find x and y.

Thank you in advance! Oh, and if possible, please explain on how to solve the question without giving out the answer as I'd like to attempt it on my own.

#### skeeter

MHF Helper
Never did well in bean-counting math (Stat) in college, but sure looks like x has to be 3 ...

#### HallsofIvy

MHF Helper
You understand why skeeter says "x has to be 3", don't you?

If you know what a "stem-and-leaf diagram" is then you know that the given data is
53, 54, 56, 58, 59, 61, 62, 64, 66, 66, 6y (this is 60+y, not "6 times y), 72, 74, 76, 77, 78, 83, 8x (again, 80+y, not 8 times y), 83, 89.

There are 20 numbers. Since that is even, the median is the average of the 10 and 11th numbers. What must "6y" be so that is 67?

#### lecloc

For y, I got (66+60+y)/2 = 67 >>> y = 8.

But I still don't understand why x = 3..

#### HallsofIvy

MHF Helper
"8x" lies between 83 and 83.