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Bar and Histograms (What Would You Use: Part 1)

Author: Brink Harrison


Time: 1 class period
Preparation Time: 5min making overheads
Materials: Rocket Thrust Data Overhead
Data Overhead
Homework
Teacher Background

Abstract
Constructing bar graphs and histograms allow students to better understand the types of data best represented by the respective graphs. Teacher and students review together the structure of bar graphs and histograms so the students will be able to choose the better graph for representing a given set of data.


Objectives

Students will be able to:-

i. Construct a bar graph given a appropriate set of data
ii. Construct a grouped frequency chart for a set of data
iii. Construct a histogram from a grouped frequency chart or given an appropriate set of data
iv. Be able to determine when to choose a bar graph or a histogram to represent a given set of data

National Science Education Standards
Data Analysis and Probability
Formulate questions that can be addressed with data and collect, organize, and display relevant data to answer them.

Measurement
Understand measurable attributes of objects and the units, systems, and processes of measurement.


Teacher Background
See attached sheet above

Related and Resource Websites
http://www.shodor.org/interactivate/lessons/sm3.html
http://nces.ed.gov/nceskids/graphing/

 

Activity

Ask the students, “What are the various types of graphs you have used in the past to represent data?” Hopefully they will name bar graphs, histograms, line graphs, and pie-graphs or some form of a similar list. Ask them, “Why are there so many different types of graphs?” (There are different types because each one has a fairly specific use). Allow time for discussion.

Tell them, “Today we’re going to look at bar graphs and histograms since you have probably made these graphs in the past. Let’s start with bar graphs. What are bar graphs used to represent? What usually goes on the horizontal axis and what goes on the vertical axis?” (See teacher background) Allow time for discussion.

If you have access to a computer laboratory or a computer with a projection screen, go to the following website http://nces.ed.gov/nceskids/graphing/bar.asp and use the education data from NCES to create a bar graph for Popular Bachelor’s Degrees, 1999-2000. Have the students discuss the structure of the bar graph and how they would read the bar graph to determine the number of each type of bachelor’s degrees awarded.

Another good website that uses bar graphs to represent the probability of getting a given number when rolling a pair of dice is http://nces.ed.gov/nceskids/probability/index.asp. The students get to put in the number of times the dice are rolled. Ask the students, “If we rolled the pair of dice many times, what would expect the bar graph to look like?” Allow time for discussion.

If in a laboratory, have the students pair up and assign each pair of students a specific number of rolls, going from 100 to 1000 by hundreds. Tell the students “Enter your number of rolls into the box and then press the “Roll Dice” button. Make a sketch of the bar graph that appears on your screen. Does this bar graph agree with your expectations?” Have them repeat the experiment with the same number of rolls. Ask, “Why is the second bar graph different from the first if you rolled the dice the same number of times in each experiment?” Allow time for discussion.

Begin a discussion about the differences between bar graphs and histograms by saying, “Histograms and bar graphs look very similar. What's different about them?” Allow time for the students to think about this and come up with suggestions. (A good website discussing the differences is http://bdaugherty.tripod.com/KeySkills/histograms.html )

In a nutshell, histograms are closely related to bar charts, but differ in that they are used represent frequency distributions. A frequency distribution is a tabular arrangement of data to whereby the data is grouped into different intervals, and then the number of observations that belong to each interval is determined. Data that is presented in this manner are known as grouped data. The smallest value that can belong to a given interval is called the lower class limit, while the largest value that can belong to the interval is called the upper class limit. The difference between the upper class limit and the lower class limit is defined to be the class width. When designing the intervals to be used in a frequency distribution, it is preferable that the class widths of all intervals be the same. (Source:http://library.thinkquest.org/10030/2sroffd.htm?tqskip1=1&tqtime=0624 )

Put up the Rocket Thrust Data overhead. The observations have already been into classes of width 3 for the students. Ask them, “How would we represent this data as a histogram? What goes along the x-axis? Do we need to start at the origin on the x-axis? What’s the lowest number we want to use on the x-axis? How wide is each class width? What goes on the y-axis? What’s the smallest number we want to use on the y-axis?” Have the students take you through the steps to create the histogram. (See http://bdaugherty.tripod.com/KeySkills/histograms.html for a picture of the histogram representing this data.)

Put up the Data overhead. Note that the values range from 0 to 10.0, therefore, it is easiest to create the following 10 classes, each with a class width of one unit.

class 1: 0 - 1.0 class 6: 5.0 - 6.0
class 2: 1.0 - 2.0 class 7: 6.0 - 7.0
class 3: 2.0 - 3.0 class 8: 7.0 - 8.0
class 4: 3.0 - 4.0 class 9: 8.0 - 9.0
class 5: 4.0 - 5.0 class 10: 9.0 - 10.0

We assume that a measurement that falls on the border between two intervals belongs to the previous interval (e.g. the value 4.0 belongs to class 4 instead of class 5).

By counting the number of observations that fall into each class, we get the following frequency distribution:

Measurements Frequency

0.0 - 1.0 3
1.0 - 2.0 4
2.0 - 3.0 4
3.0 - 4.0 7
4.0 - 5.0 6
5.0 - 6.0 5
6.0 - 7.0 5
7.0 - 8.0 1
8.0 - 9.0 2
9.0 - 10.0 3

(Source:http://library.thinkquest.org/10030/2sroffd.htm?tqskip1=1&tqtime=0624 )



Homework

1. Have the students do the Activity Sheet where they must decide if they would choose a bar graph or a histogram to represent the data.

Situation Bar Graph or
Histogram?
Reasoning
We want to compare the
total revenues of five different companies.
Bar Graph No bins involved - you look at each company separately
We have measured revenues of several companies. We want to compare numbers of companies that make from 0 to 10,000; from 10,000 to 20,000; from 20,000 to 30,000 and so on. Histogram You want to know the number of companies are in each revenue bin
We want to compare heights of ten oak trees in a city park Bar Graph No bins involved – you look at each tree separately
We have measured several trees in a city park. We want to compare numbers of trees that are from 0 to 5 meters high; from 5 to 10; from 10 to 15 and so on. Histogram You want to know the number of trees are in each height bin

(Adapted from: http://www.shodor.org/interactivate/discussions/sd4.html)

2. Have the students do problems 1 and 2 from the website:
http://www.shodor.org/interactivate/lessons/st5.html

Embedded Assessment

Student understanding of bar graphs can be assessed through informal discussions with the class about the structure and use of bar graphs and informal observations as the students make bar graphs to represent the probabilities of getting a certain number when rolling dice a given number of times.

Student understanding of histograms can be assessed through informal discussions about the structure of histograms and how they represent the data of a grouped frequency chart. As a given student leads the teacher through the steps to draw a histogram from a given frequency chart, other students should be doing a self-evaluation to see how well they understand the procedure. Informal observations as the students make a histogram from a given set of data, without being given a frequency chart, can be used to assess how well the students understand the process of making a histogram.

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 


PULSE is a project of the Community Outreach and Education Program of the Southwest Environmental Health Sciences Center and is funded by:


an
NIH/NCRR award #16260-01A1
The Community Outreach and Education Program is part of the Southwest Environmental Health Sciences Center: an NIEHS Award

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Supported by NIEHS grant # ES06694


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