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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.

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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
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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.

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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.

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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.

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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

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.
anyone know any internet site where one can find nanotechnology papers?
Damian Reply
sciencedirect big data base
Introduction about quantum dots in nanotechnology
Praveena Reply
what does nano mean?
Anassong Reply
nano basically means 10^(-9). nanometer is a unit to measure length.
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
Damian Reply
absolutely yes
how to know photocatalytic properties of tio2 nanoparticles...what to do now
Akash Reply
it is a goid question and i want to know the answer as well
characteristics of micro business
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Do somebody tell me a best nano engineering book for beginners?
s. Reply
there is no specific books for beginners but there is book called principle of nanotechnology
what is fullerene does it is used to make bukky balls
Devang Reply
are you nano engineer ?
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
what is the actual application of fullerenes nowadays?
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
what is the Synthesis, properties,and applications of carbon nano chemistry
Abhijith Reply
Mostly, they use nano carbon for electronics and for materials to be strengthened.
is Bucky paper clear?
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
so some one know about replacing silicon atom with phosphorous in semiconductors device?
s. Reply
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Do you know which machine is used to that process?
how to fabricate graphene ink ?
for screen printed electrodes ?
What is lattice structure?
s. Reply
of graphene you mean?
or in general
in general
Graphene has a hexagonal structure
On having this app for quite a bit time, Haven't realised there's a chat room in it.
what is biological synthesis of nanoparticles
Sanket Reply
what's the easiest and fastest way to the synthesize AgNP?
Damian Reply
how did you get the value of 2000N.What calculations are needed to arrive at it
Smarajit Reply
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1 It is estimated that 30% of all drivers have some kind of medical aid in South Africa. What is the probability that in a sample of 10 drivers: 3.1.1 Exactly 4 will have a medical aid. (8) 3.1.2 At least 2 will have a medical aid. (8) 3.1.3 More than 9 will have a medical aid.
Nerisha Reply
Practice Key Terms 1

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Source:  OpenStax, Collaborative statistics. OpenStax CNX. Jul 03, 2012 Download for free at http://cnx.org/content/col10522/1.40
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