Stem-and-leaf plot

Question

I need help on making and solving stem-and-leaf plots

Answer 1

Daeja,

 

This is how you make a stem and leaf plot:

 

Say you are given the following information (just a bunch of random numbers):

 

12,15,18,17,16,22,25,27,29,22,24,21,18,19,15,17,31,34,35,38,24,22,25,26,27,21,15,16,19

 

What you're going to do is create the "stems" for this information, in this case you'll have a 10 stem, a 20 stem, and a 30 stem.

Write your stems like this:

 

Stem

1

 

2

 

3

 

Next, you will write your "leafs" in a row next to your stems (at first write them in the order they're given so you don't miss any).

 

Stem      Leaf

1            2,5,8,7,6,8,9,5,7,5,6,9

 

2            2,5,7,9,2,4,1,4,2,5,6,7,1

 

3            1,4,5,8

 

Finally, put your leafs in numerical order from smallest to largest

 

Stem     Leaf

1           2,5,5,5,6,6,7,7,8,8,9,9

 

2           1,1,2,2,2,4,4,5,5,6,7,7,9

 

3           1,4,5,8

 

Voila!  You have a stem and leaf plot!

 

Answer 2

Stem-and-leaf plots are a method for showing the frequency with which certain classes of values occur. You could make a frequency distribution table or a histogram for the values, or you can use a stem-and-leaf plot and let the numbers themselves to show pretty much the same information.

For instance, suppose you have the following list of values: 12, 13, 21, 27, 33, 34, 35, 37, 40, 40, 41. You could make a frequency distribution table showing how many tens, twenties, thirties, and forties you have:

Frequency Frequency
Class

10 - 19          2
20 - 29          2
30 - 39          4
40 - 49          3

You could make a histogram, which is a bar-graph showing the number of occurrences, with the classes being numbers in the tens, twenties, thirties, and forties:


The downside of frequency distribution tables and histograms is that, while the frequency of each class is easy to see, the original data points have been lost. You can tell, for instance, that there must have been three listed values that were in the forties, but there is no way to tell from the table or from the histogram what those values might have been.

On the other hand, you could make a stem-and-leaf plot for the same data:

stem-and-leaf plot


Stem   Leaf

  1       2 3
  2       1 7
  3       3 4 5 7
  4       0 0 1

The "stem" is the left-hand column which contains the tens digits. The "leaves" are the lists in the right-hand column, showing all the ones digits for each of the tens, twenties, thirties, and forties. As you can see, the original values can still be determined; you can tell, from that bottom leaf, that the three values in the forties were 40, 40, and 41.

Note that basically what stem and leaf plot does is just divide the two-digit to one-digit format, where the first digit as the stem and the second digit as the leaf. The leaves show the frequency. Notice the pattern. For example, 12, 1 is the stem and leaf is 2.

I hope this would help you understand the stem and leaf plot.

Best Regards
Dulshan De Silva