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2.3: Stem-and-Leaf Displays

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    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 \(\PageIndex{1}\)

    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-and-Leaf Graph
    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% \(\left(\frac{8}{31}\right)\) were in the 90s or 100, a fairly high number of As.

    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.

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

    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 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.

    Another type of graph that is useful for specific data values is a line graph. In the particular line graph shown in Example, the x-axis (horizontal axis) consists of data values and the y-axis (vertical axis) consists of frequency points. The frequency points are connected using line segments.

    Example \(\PageIndex{7}\)

    In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his or her chores. The results are shown in Table and in Figure.

    Number of times teenager is reminded Frequency
    0 2
    1 5
    2 8
    3 14
    4 7
    5 4
    A line graph showing the number of times a teenager needs to be reminded to do chores on the x-axis and  frequency on the y-axis.
    Figure \(\PageIndex{1}\)

    Bar graphs consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes (used in three-dimensional plots), and they can be vertical or horizontal. The bar graph shown in Example \(\PageIndex{9}\) has age groups represented on the x-axis and proportions on the y-axis.

    Example \(\PageIndex{9}\)

    By the end of 2011, Facebook had over 146 million users in the United States. Table shows three age groups, the number of users in each age group, and the proportion (%) of users in each age group. Construct a bar graph using this data.

    Age groups Number of Facebook users Proportion (%) of Facebook users
    13–25 65,082,280 45%
    26–44 53,300,200 36%
    45–64 27,885,100 19%


    This is a bar graph that matches the supplied data. The x-axis shows age groups,  and the y-axis shows the percentages of Facebook users.
    Figure \(\PageIndex{3}\).

    Exercise \(\PageIndex{10}\)

    The population in Park City is made up of children, working-age adults, and retirees. Table shows the three age groups, the number of people in the town from each age group, and the proportion (%) of people in each age group. Construct a bar graph showing the proportions.

    Age groups Number of people Proportion of population
    Children 67,059 19%
    Working-age adults 152,198 43%
    Retirees 131,662 38%


    This is a bar graph that matches the supplied data. The x-axis shows age groups, and the y-axis shows the percentages of Park City's population.
    Figure \(\PageIndex{4}\).


    A stem-and-leaf plot is a way to plot data and look at the distribution. In a stem-and-leaf plot, all data values within a class are visible. The advantage in a stem-and-leaf plot is that all values are listed, unlike a histogram, which gives classes of data values. A line graph is often used to represent a set of data values in which a quantity varies with time. These graphs are useful for finding trends. That is, finding a general pattern in data sets including temperature, sales, employment, company profit or cost over a period of time. A bar graph is a chart that uses either horizontal or vertical bars to show comparisons among categories. One axis of the chart shows the specific categories being compared, and the other axis represents a discrete value. Some bar graphs present bars clustered in groups of more than one (grouped bar graphs), and others show the bars divided into subparts to show cumulative effect (stacked bar graphs). Bar graphs are especially useful when categorical data is being used.

    WeBWorK Problems

    Query \(\PageIndex{1}\)

    Query \(\PageIndex{2}\)

    Query \(\PageIndex{3}\)

    Query \(\PageIndex{4}\)

    Query \(\PageIndex{5}\)

    Query \(\PageIndex{6}\)

    Query \(\PageIndex{7}\)



    1. Burbary, Ken. Facebook Demographics Revisited – 2001 Statistics, 2011. Available online at (accessed August 21, 2013).
    2. “9th Annual AP Report to the Nation.” CollegeBoard, 2013. Available online at (accessed September 13, 2013).
    3. “Overweight and Obesity: Adult Obesity Facts.” Centers for Disease Control and Prevention. Available online at (accessed September 13, 2013).

    Contributors and Attributions

    • Barbara Illowsky and Susan Dean (De Anza College) with many other contributing authors. Content produced by OpenStax College is licensed under a Creative Commons Attribution License 4.0 license. Download for free at

    • CUNY OER WeBWorK Fellows

    This page titled 2.3: Stem-and-Leaf Displays is shared under a CC BY 4.0 license and was authored, remixed, and/or curated by OpenStax via source content that was edited to the style and standards of the LibreTexts platform; a detailed edit history is available upon request.