71 86 63 46 70 63 49 63 81 71 63 59 45 63 70 64 

Arrange them in order smallest to largest: 

45 46 49 59 63 63 63 63 63 64 70 70 71 71 81 86

Put the 40's on the first row, the 50's on the 
2nd row, the 60's on the 3rd row, etc:

45 46 49
59
63 63 63 63 63 64
70 70 71 71
81 86

Draw a line between the digits of the left-most number
on each row:

4|5 46 49
5|9
6|3 63 63 63 63 64
7|0 70 71 71
8|1 86

Erase the first digit of all the other numbers:

4|5 6 9
5|9
6|3 3 3 3 3 4
7|0 0 1 1
8|1 6

Take out the spaces between the digits:

4|569
5|9
6|333334
7|0011
8|16



That's it.  It's sort of a sideways histogram. 
If you turn your head 90° to the right, 
(or if you have it printed on paper, turn the paper 90°
to the left), you'll see that the stem-and-leaf 
plot looks a lot like a histogram.

Edwin