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What is a stem-and-leaf plot?. It's a type of graph.It displays every piece of data in a large set of data.It shows how many pieces of data fall into various intervals.. How can you make a stem-and-leaf plot?. First you need some data, such as the average temperature (in ?F) in January in 22
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1. Stem-and-Leaf Plot What is it?
How can you make one?
What does it tell you?
2. What is a stem-and-leaf plot? It’s a type of graph.
It displays every piece of data in a large set of data.
It shows how many pieces of data fall into various intervals.
3. How can you make a stem-and-leaf plot? First you need some data, such as the average temperature (in şF) in January in 22 major U.S. cities:
38, 5, 21, 16, 44, 49, 62, 13, 29, 52, 57,
68, 78, 9, 30, 39, 62, 15, 28, 50, 11, 56
4. You will begin by making an “unordered” stem-and-leaf plot.
An unordered stem-and-leaf plot is like a
first draft. It will help you get organized.
5. Now take a look at the data.
Notice that that the smallest number is 5
and the largest number is 78.
38, 5, 21, 16, 44, 49, 62, 13, 29, 52, 57,
68, 78, 9, 30, 39, 62, 15, 28, 50, 11, 56
6. Decide what should be the “stems”
38, 05, 21, 16, 44, 49, 62, 13, 29, 52, 57,
68, 78, 09, 30, 39, 62, 15, 28, 50, 11, 56
Let the stems be the tens digits from 0 to 7.
7. List the stems List the stems vertically from smallest to largest.
0
1
2
3
4
5
6
7
8. List the stems List the stems vertically from smallest to largest.
Draw a vertical
line segment
next to the stems.
0
1
2
3
4
5
6
7
9. Now you are ready to add the “leaves”
The units digit of each number is its leaf.
The lowest temperature, 5, has a stem of 0.
The units digit is 5: 5 is the leaf.
The highest temperature, 78, has a stem of 7.
The units digit is 8: 8 is the leaf.
10. List each leaf on the same line as its corresponding stem. 0
1
2
3 8
4
5
6
7
11. List each leaf on the same line as its corresponding stem. 0 5
1
2
3 8
4
5
6
7
12. List each leaf on the same line as its corresponding stem. 0 5
1
2 1
3 8
4
5
6
7
13. List each leaf on the same line as its corresponding stem. 0 5
1 6
2 1
3 8
4
5
6
7
14. List each leaf on the same line as its corresponding stem. 0 5
1 6
2 1
3 8
4 4
5
6
7
15. List each leaf on the same line as its corresponding stem. 0 5
1 6
2 1
3 8
4 4 9
5
6
7
16. List each leaf on the same line as its corresponding stem. 0 5
1 6
2 1
3 8
4 4 9
5
6 2
7
17. You might want to cross out each number as you add each leaf to the stem-and-leaf plot.
38, 5, 21, 16, 44, 49, 62, 13, 29, 52, 57,
68, 78, 9, 30, 39, 62, 15, 28, 50, 11, 56
18. Finish adding all the leaves to the plot. 0 5 9
1 6 3 5 1
2 1 9 8
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
19. Count to be sure that you have included all the leaves. (There are 22 leaves.) 0 5 9
1 6 3 5 1
2 1 9 8
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
20. This is your “unordered” plot. The leaves are not in numerical order. 0 5 9
1 6 3 5 1
2 1 9 8
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
21. Now order the leaves from least to greatest. 0 5 9
1 6 3 5 1
2 1 9 8
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
22. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 9 8
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
23. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 8 0 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
24. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
25. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 2 7 0 6
6 2 8 2
7 8
26. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 8 2
7 8
27. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
28. Now order the leaves from least to greatest. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
29. This is an “ordered” plot. 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
30. Add a “key”
31. Add a “key”
32. Add a “key” Key: 7 8 means 78şF
33. And finally add a title…
34. And finally add a title…
Average Temperature (şF) in January in 22 major U.S. Cities
35. Average Temperature (şF) in January in 22 major U.S. Cities 0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
36. A Stem-and-Leaf Plot Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
37. What does a stem-and-leaf plot tell you? Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
38. The extremes Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
39. 5 Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
40. and 78 Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
41. A stem-and-leaf plot makes it easy to find one or more modes. Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
42. Recall that a mode is a “measure of central tendency”.
The mode is the value that occurs
most often in a set of data.
Sometimes there are two modes.
Sometimes there is no mode.
43. This stem-and-leaf plot has one mode. Can you find it? Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
44. It’s 62 Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
45. It’s 62 Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
46. What do you look for?
Look for the leaf that occurs the most times
in one row.
47. Look one more time. Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
48. There’s one more thing about a stem-and-leaf plot…
All of the data values are shown.
49. A Stem-and-Leaf Plot Average Temperature (şF) in January in 22 major U.S. Cities
0 5 9
1 1 3 5 6
2 1 8 9
3 0 8 9
4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 7 8 means 78şF
50. Just one last thing! Sometimes you might…
see
or need to create
or need to be able to read…
a double stem-and-leaf plot.
51. Here’s a Double Stem-and-Leaf Plot Average Temperature (şF) in January
in 22 major Canadian Cities vs. U.S. Cities
Canada USA
9 8 6 3 2 0 5 9
8 7 5 5 4 3 2 1 1 3 5 6
7 4 3 3 0 2 1 8 9
5 2 0 3 0 8 9
6 1 4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 3 9 means 39şF
2 3 means 32şF
52. Make an observation about the way the Canadian temperatures are ordered. Average Temperature (şF) in January
in 22 major Canadian Cities vs. U.S. Cities
Canada USA
9 8 6 3 2 0 5 9
8 7 5 5 4 3 2 1 1 3 5 6
7 4 3 3 0 2 1 8 9
5 2 0 3 0 8 9
6 1 4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 3 9 means 39şF
2 3 means 32şF
53. Make an observation about the key. Average Temperature (şF) in January
in 22 major Canadian Cities vs. U.S. Cities
Canada USA
9 8 6 3 2 0 5 9
8 7 5 5 4 3 2 1 1 3 5 6
7 4 3 3 0 2 1 8 9
5 2 0 3 0 8 9
6 1 4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 3 9 means 39şF
2 3 means 32şF
54. Any other observations? Questions? Average Temperature (şF) in January
in 22 major Canadian Cities vs. U.S. Cities
Canada USA
9 8 6 3 2 0 5 9
8 7 5 5 4 3 2 1 1 3 5 6
7 4 3 3 0 2 1 8 9
5 2 0 3 0 8 9
6 1 4 4 9
5 0 2 6 7
6 2 2 8
7 8
Key: 3 9 means 39şF
2 3 means 32şF
55. Then we are ready to go!
This PowerPoint is on the
8th grade math home page.
Click on
MCAS WORKSHOP RESOURCES.
