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, 23 has stem two and leaf three. The number 432 has stem 43 and leaf two. Likewise, the number 5,432 has stem 543 and leaf two. The decimal 9.3 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):
33; 42; 49; 49; 53; 55; 55; 61; 63; 67; 68; 68; 69; 69; 72; 73; 74; 78; 80; 83; 88; 88; 88; 90; 92; 94; 94; 94; 94; 96; 100

Stem Leaf
3 3
4 2 9 9
5 3 5 5
6 1 3 7 8 8 9 9
7 2 3 4 8
8 0 3 8 8 8
9 0 2 4 4 4 4 6
10 0

The stemplot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% (831) were in the 90s or 100, 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):

32; 32; 33; 34; 38; 40; 42; 42; 43; 44; 46; 47; 47; 48; 48; 48; 49; 50; 50; 51; 52; 52; 52; 53; 54; 56; 57; 57; 60; 61

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 to not to fit the pattern of the graph. Some outliers are due to mistakes (for example, writing down 50 instead of 500) 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:

1.1; 1.5; 2.3; 2.5; 2.7; 3.2; 3.3; 3.3; 3.5; 3.8; 4.0; 4.2; 4.5; 4.5; 4.7; 4.8; 5.5; 5.6; 6.5; 6.7; 12.3;
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:

0.5; 0.7; 1.1; 1.2; 1.2; 1.3; 1.3; 1.5; 1.5; 1.7; 1.7; 1.8; 1.9; 2.0; 2.2; 2.5; 2.6; 2.8; 2.8; 2.8; 3.5; 3.8; 4.4; 4.8; 4.9; 5.2; 5.5; 5.7; 5.8; 8.0

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

Example

The table shows the number of wins and losses the Atlanta Hawks have had in 42 seasons. Create a side-by-side stem-and-leaf plot of these wins and losses.

Losses Wins Year Losses Wins Year
34 48 1968–1969 41 41 1989–1990
34 48 1969–1970 39 43 1990–1991
46 36 1970–1971 44 38 1991–1992
46 36 1971–1972 39 43 1992–1993
36 46 1972–1973 25 57 1993–1994
47 35 1973–1974 40 42 1994–1995
51 31 1974–1975 36 46 1995–1996
53 29 1975–1976 26 56 1996–1997
51 31 1976–1977 32 50 1997–1998
41 41 1977–1978 19 31 1998–1999
36 46 1978–1979 54 28 1999–2000
32 50 1979–1980 57 25 2000–2001
51 31 1980–1981 49 33 2001–2002
40 42 1981–1982 47 35 2002–2003
39 43 1982–1983 54 28 2003–2004
42 40 1983–1984 69 13 2004–2005
48 34 1984–1985 56 26 2005–2006
32 50 1985–1986 52 30 2006–2007
25 57 1986–1987 45 37 2007–2008
32 50 1987–1988 35 47 2008–2009
30 52 1988–1989 29 53 2009–2010