Finding x and y in stem-and-leaf diagram

Dec 2014
6
0
HK
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
Jun 2008
16,217
6,765
North Texas
Never did well in bean-counting math (Stat) in college, but sure looks like x has to be 3 ... ;)
 

HallsofIvy

MHF Helper
Apr 2005
20,249
7,909
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?
 
Dec 2014
6
0
HK
For y, I got (66+60+y)/2 = 67 >>> y = 8.

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