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This module introduces the use of stem-and-leaf graphs (stemplots), line graphs and bar graphs for describing a set of data visually.

One simple graph, the stem-and-leaf graph or stem plot , 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 2 and leaf 3. Four hundred thirty-two (432) has stem 43 and leaf 2. Five thousand four hundred thirty-two (5,432) has stem 543 and leaf 2. The decimal 9.3 has stem 9 and leaf 3. Write the stems in a vertical line from smallest the largest. Draw a vertical line to the right of the stems. Then write the leaves in increasing order next to their corresponding stem.

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 diagram
Stem Leaf
3 3
4 299
5 355
6 1378899
7 2348
8 03888
9 0244446
10 0

The stem plot shows that most scores fell in the 60s, 70s, 80s, and 90s. Eight out of the 31 scores or approximately 26% of the scores were in the 90's or 100, a fairly high number of As.

The stem plot is a quick way to graph 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. In the example above, there were no outliers.

Create a stem plot 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

The data are the distance (in kilometers) from a home to the nearest supermarket.

  1. Are there any values that might possibly be outliers?
  2. Do the data seem to have any concentration of values?
The leaves are to the right of the decimal.

The value 12.3 may be an outlier. Values appear to concentrate at 3 and 4 kilometers.

Stem Leaf
1 1 5
2 3 5 7
3 2 3 3 5 8
4 0 2 5 5 7 8
5 5 6
6 5 7
12 3

Another type of graph that is useful for specific data values is a line graph . In the particular line graph shown in the example, the x-axis consists of data values and the y-axis consists of frequency points . The frequency points are connected.

In a survey, 40 mothers were asked how many times per week a teenager must be reminded to do his/her chores. The results are shown in the table and the line graph.

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.

Bar graphs consist of bars that are separated from each other. The bars can be rectangles or they can be rectangular boxes and they can be vertical or horizontal.

The bar graph shown in Example 4 has age groups represented on the x-axis and proportions on the y-axis .

By the end of 2011, in the United States, Facebook had over 146 million users. The table shows three age groups, the number of users in each age group and the proportion (%) of users in each age group. Source: http://www.kenburbary.com/2011/03/facebook-demographics-revisited-2011-statistics-2/

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%

A bar graph showing age groups on the x-axis and percentages of Facebook users on the y-axis.

The columns in the table below contain the race/ethnicity of U.S. Public Schools: High School Class of 2011, percentages for the Advanced Placement Examinee Population for that class and percentages for the Overall Student Population. The 3-dimensional graph shows the Race/Ethnicity of U.S. Public Schools (qualitative data) on the x-axis and Advanced Placement Examinee Population percentages on the y-axis . ( Source: http://www.collegeboard.com and Source: http://apreport.collegeboard.org/goals-and-findings/promoting-equity )

Race/Ethnicity AP Examinee Population Overall Student Population
1 = Asian, Asian American or Pacific Islander 10.3% 5.7%
2 = Black or African American 9.0% 14.7%
3 = Hispanic or Latino 17.0% 17.6%
4 = American Indian or Alaska Native 0.6% 1.1%
5 = White 57.1% 59.2%
6 = Not reported/other 6.0% 1.7%

A bar graph showing race and ethnicity on the x-axis and percentages of AP examinees on the y-axis.

Go to Outcomes of Education Figure 22 for an example of a bar graph that shows unemployment rates of persons 25 years and older for 2009.

This book contains instructions for constructing a histogram and a box plot for the TI-83+ and TI-84 calculators. You can find additional instructions for using these calculators on the Texas Instruments (TI) website .

Questions & Answers

where we get a research paper on Nano chemistry....?
Maira Reply
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
what are the products of Nano chemistry?
Maira Reply
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Preparation and Applications of Nanomaterial for Drug Delivery
Hafiz Reply
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
Jyoti Reply
I only see partial conversation and what's the question here!
Crow Reply
what about nanotechnology for water purification
RAW Reply
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
yes that's correct
I think
Nasa has use it in the 60's, copper as water purification in the moon travel.
nanocopper obvius
what is the stm
Brian Reply
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
scanning tunneling microscope
how nano science is used for hydrophobicity
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
what is differents between GO and RGO?
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
analytical skills graphene is prepared to kill any type viruses .
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
what is Nano technology ?
Bob Reply
write examples of Nano molecule?
The nanotechnology is as new science, to scale nanometric
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
what king of growth are you checking .?
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
Stoney Reply
why we need to study biomolecules, molecular biology in nanotechnology?
Adin Reply
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
what school?
biomolecules are e building blocks of every organics and inorganic materials.
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Source:  OpenStax, Collaborative statistics (with edits: teegarden). OpenStax CNX. Jul 20, 2009 Download for free at http://legacy.cnx.org/content/col10561/1.3
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