Stem-and-Leaf Graphs (Stemplots)

Learning Outcomes

  • Display data graphically and interpret graphs: stemplots, histograms, and box plots.


One simple graph, the stem-and-leaf graph or stemplot, comes from the field of exploratory data analysis. It is a good choice when the data sets are small. To create the plot, divide each observation of data into a stem and a leaf. The leaf consists of a final significant digit. For example,
2323
has stem two and leaf three. The number
432432
has stem
4343
and leaf two. Likewise, the number
5,4325,432
has stem
543543
and leaf two. The decimal
9.39.3
has stem nine and leaf three. Write the stems in a vertical line from smallest to largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.

Example

For Susan Dean's spring pre-calculus class, scores for the first exam were as follows (smallest to largest):

3333
;
4242
;
4949
;
4949
;
5353
;
5555
;
5555
;
6161
;
6363
;
6767
;
6868
;
6868
;
6969
;
6969
;
7272
;
7373
;
7474
;
7878
;
8080
;
8383
;
8888
;
8888
;
8888
;
9090
;
9292
;
9494
;
9494
;
9494
;
9494
;
9696
;
100100


Stem Leaf
33
33
44
22
99
99
55
33
55
55
66
11
33
77
88
88
99
99
77
22
33
44
88
88
00
33
88
88
88
99
00
22
44
44
44
44
66
1010
00
The stemplot shows that most scores fell in the
6060
s,
7070
s,
8080
s, and
9090
s. Eight out of the
3131
scores or approximately
2626
% (
831\frac{8}{31}
) were in the
9090
s or
100100
, a fairly high number of As.

Try It

For the Park City basketball team, scores for the last 30 games were as follows (smallest to largest):

3232
;
3232
;
3333
;
3434
;
3838
;
4040
;
4242
;
4242
;
4343
;
4444
;
4646
;
4747
;
4747
;
4848
;
4848
;
4848
;
4949
;
5050
;
5050
;
5151
;
5252
;
5252
;
5252
;
5353
;
5454
;
5656
;
5757
;
5757
;
6060
;
6161


Construct a stem plot for the data.





The stemplot is a quick way to graph data and gives an exact picture of the data. You want to look for an overall pattern and any outliers. An outlier is an observation of data that does not fit the rest of the data. It is sometimes called an extreme value. When you graph an outlier, it will appear not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down
5050
instead of
500500
) while others may indicate that something unusual is happening. It takes some background information to explain outliers, so we will cover them in more detail later.

Example

The data are the distances (in kilometers) from a home to local supermarkets. Create a stemplot using the data:

1.11.1
;
1.51.5
;
2.32.3
;
2.52.5
;
2.72.7
;
3.23.2
;
3.33.3
;
3.33.3
;
3.53.5
;
3.83.8
;
4.04.0
;
4.24.2
;
4.54.5
;
4.54.5
;
4.74.7
;
4.84.8
;
5.55.5
;
5.65.6
;
6.56.5
;
6.76.7
;
12.312.3
;

Does the data seem to have any concentration of values?

NOTE

The leaves are to the right of the decimal.





try it

The following data show the distances (in miles) from the homes of off-campus statistics students to the college. Create a stem plot using the data and identify any outliers:

0.50.5
;
0.70.7
;
1.11.1
;
1.21.2
;
1.21.2
;
1.31.3
;
1.31.3
;
1.51.5
;
1.51.5
;
1.71.7
;
1.71.7
;
1.81.8
;
1.91.9
;
2.02.0
;
2.22.2
;
2.52.5
;
2.62.6
;
2.82.8
;
2.82.8
;
2.82.8
;
3.53.5
;
3.83.8
;
4.44.4
;
4.84.8
;
4.94.9
;
5.25.2
;
5.55.5
;
5.75.7
;
5.85.8
;
8.08.0






Watch this video to see an example of how to create a stem plot.



Example

A side-by-side stem-and-leaf plot allows a comparison of the two data sets in two columns. In a side-by-side stem-and-leaf plot, two sets of leaves share the same stem. The leaves are to the left and the right of the stems. The two following tables show the ages of presidents at their inauguration and at their death. Construct a side-by-side stem-and-leaf plot using this data.

Presidential Ages at Inauguration:

President Age President Age President Age
Washington
5757
Lincoln
5252
Hoover
5454
J. Adams
6161
A. Johnson
5656
F. Roosevelt
5151
Jefferson
5757
Grant
4646
Truman
6060
Madison
5757
Hayes
5454
Eisenhower
6262
Monroe
5858
Garfield
4949
Kennedy
4343
J. Q. Adams
5757
Arthur
5151
L. Johnson
5555
Jackson
6161
Cleveland
4747
Nixon
5656
Van Buren
5454
B. Harrison
5555
Ford
6161
W. H. Harrison
6868
Cleveland
5555
Carter
5252
Tyler
5151
McKinley
5454
Reagan
6969
Polk
4949
T. Roosevelt
4242
G.H.W. Bush
6464
Taylor
6464
Taft
5151
Clinton
4747
Fillmore
5050
Wilson
5656
G. W. Bush
5454
Pierce
4848
Harding
5555
Obama
4747
Buchanan
6565
Coolidge
5151
Presidential Age at Death:

President Age President Age President Age
Washington
6767
Lincoln
5656
Hoover
9090
J. Adams
9090
A. Johnson
6666
F. Roosevelt
6363
Jefferson
8383
Grant
6363
Truman
8888
Madison
8585
Hayes
7070
Eisenhower
7878
Monroe
7373
Garfield
4949
Kennedy
4646
J. Q. Adams
8080
Arthur
5656
L. Johnson
6464
Jackson
7878
Cleveland
7171
Nixon
8181
Van Buren
7979
B. Harrison
6767
Ford
9393
W. H. Harrison
6868
Cleveland
7171
Reagan
9393
Tyler
7171
McKinley
5858
Polk
5353
T. Roosevelt
6060
Taylor
6565
Taft
7272
Fillmore
7474
Wilson
6767
Pierce
6464
Harding
5757
Buchanan
7777
Coolidge
6060

Example

The table shows the number of wins and losses the Atlanta Hawks have had in
4242
seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.

Losses Wins Year Losses Wins Year
3434
4848
1968–1969
4141
4141
1989–1990
3434
4848
1969–1970
3939
4343
1990–1991
4646
3636
1970–1971
4444
3838
1991–1992
4646
3636
1971–1972
3939
4343
1992–1993
3636
4646
1972–1973
2525
5757
1993–1994
4747
3535
1973–1974
4040
4242
1994–1995
5151
3131
1974–1975
3636
4646
1995–1996
5353
2929
1975–1976
2626
5656
1996–1997
5151
3131
1976–1977
3232
5050
1997–1998
4141
4141
1977–1978
1919
3131
1998–1999
3636
4646
1978–1979
5454
2828
1999–2000
3232
5050
1979–1980
5757
2525
2000–2001
5151
3131
1980–1981
4949
3333
2001–2002
4040
4242
1981–1982
4747
3535
2002–2003
3939
4343
1982–1983
5454
2828
2003–2004
4242
4040
1983–1984
6969
1313
2004–2005
4848
3434
1984–1985
5656
2626
2005–2006
3232
5050
1985–1986
5252
3030
2006–2007
2525
5757
1986–1987
4545
3737
2007–2008
3232
5050
1987–1988
3535
4747
2008–2009
3030
5252
1988–1989
2929
5353
2009–2010




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