Download Statistics, Probability (Aga)

DATA ANALYSIS, STATISTICS AND
PROBABILITY
MATH 150
PROF. CHRISTINE VON RENESSE
OCTOBER 16, 2007
BY
AGNIESZKA KUBRAK
Agnieszka Kubrak
Math 150
Project
October 16, 2007
DATA ANALYSIS, STATISTICS AND PROBABILITY
Grades 3-4
Goals: The students will be able to select and use appropriate statistical method to
analyze data.
Objectives:
1. The students will collect data using survey.
2. The students will represent data using bar graphs.
3. The students will measure the center with the focus on the median.
4. The students will predict the probability of outcomes with a change of variable.
The description of activity:
In the opening to the activity I would introduce, and enforce through out, different
mathematical terms and definitions. At first we would talk about population , samples,
and random assignment. In a bag, I would place 10 blue tokens, 10 red tokens, and 10
yellow tokens; that would be the population. Then we would take 9 and then 12 tokens
out of the bag and examine the amount of tokens of each of the colors; that would be the
sample. During the activity, we would talk about the sample size, the randomness, and
representation. (To make this activity more appealing to younger students I would use
different manipulative, such as color beads, shells, candy, etc.)
Before the students would proceed to their assignments, we would write down the
steps of the activity in order they need to be completed, as a guide for the activity. I
would also provide visual aids so the students could see the expected outcome of the
lesson. Since the activity is designed for students to work in independent groups, the
written guide and visual aids would support and help in organizing their work. This
design of activity would also allow me/the teacher to spend time with each group
individually, talk about the procedures and outcomes, and make my help available
through out.
The class, based on what we spoke about sample previously, would be divided into
four to six groups; depending on amount of students in the class, so each group can be
assembled of five or six students. Every group would be responsible for collecting data
from their peers within their group. One of the students in a group would be responsible
for asking questions, and one student would be responsible for recording the answers. In
the beginning, the students would write down the answers on a paper next to the name of
each member of the group. A member of a group will ask his or her friends how many
hours a day they spend on the particular activity.
The groups would be assigned different categories: sleeping, eating, school, chores,
homework/reading, TV/play. Once each group is finished with collecting data through
the survey, they will organize data according to the amount of hours; from large to small.
Next, the students would graph their data using a bar graph. In this part of activity,
students will be provided a web site with program for designing bar graphs. To create the
graphs the students would enter the names of members of their group on the x-axis, and
the hours (24) on the y-axis. They would also label the graph based on the category the
group was assigned. The website I found for this task is rather self explanatory, and the
making of a graph is divided into few sections to make the process less confusing.
After all the groups are finished with their tasks, the class would get together and
place all the bar graphs on the board. Then we would discuss the procedures, the steps
we had to go through, we would analyze the data and what it represents. As a class, we
will also converse about the meaning of previously discussed definition and we would
provide examples of the concepts from the lesson.
Finally, the students will be asked to predict how the data within the different
categories would change if we change a variable, for instance: summer vacation,
weekends, last two weeks of school, or before exams. After that, the students will
collect the data in their groups the same way they did previously, but this time with the
consideration of one of the variables above. Once they are done with this part of the
assignment, we would meet together again to compare our previous results with the new
ones.
As continuity to the activity, the students can create a bar graph of their own day.
Each student will record data for their own day including each of the categories. Based
on the 24 hour day, they would provide information on how they spend their time. Then
with the use of web site, the students can create their bar graphs. During recording data,
the student can use the manipulatives. For instance, a student would divide a piece of
paper into 6 separate columns for each of the categories, next she or he would take 24
tokens, each representing one hour. To create a data for the entire day the student would
place each token on the appropriate space on the paper. Next, she or he would count
them and record the number representing the amount of hours. Depending on students’
familiarity with the subject, this section could be assigned as homework, or could be done
in the classroom.
To provide students with more time to practice the data collection and the data
analysis, we would replicate this type of project to find an answer to different question.
For instance, we could collect data on amount of individuals in families, pets, hobbies
and interests, favorite movies or books, etc. In addition, ones the students are
comfortable with data collection and bar graph technique, we could start to introduce
other ways of representing data, such as line graph, or pie chart. At the beginning, we
could even use our data from previous research and create new ones later on.
GLOSSARY
DATA- Data are a set of values for a measured variable.
MEDIAN- The median of a data set is the value in the center of an ordered list of the
data. It is also the value for which there are as many values above it as there are below it.
For example, in the data set {1, 1, 2, 2, 3, 3, 4, 4, 4, 5, 26}, the sixth value has five above
it and five below it. This value, 3, is the median. If a data set contains an even number of
values, the median is found by taking the mean of the two values in the center of the
ordered list; for example {1, 1, 2, 2, 2, 3, 4, 4, 4, 5}2+3=5, dived by 2, the median is
equal 2.5.
VARIABLE- A variable is a characteristic that may change (i.e., vary) from one
observation to another.
QUANTITATIVE DATA- Quantitative data are the values of a measured quantitative
variable.
QUANTITATIVE VARIABLE- Quantitative variables represent numbers or quantities,
for example, the number of lions in a box of animal crackers, or the height of each
student in a classroom.
POPULATION- The population is the entire group that a study wants information about.
RANDOM ASSIGNMENT- In a comparative experimental study, random assignment is
frequently used to select the group in which participants are placed; this is done to reduce
bias. For example, if an experiment attempted to study the effect of fear on people's
ability to think clearly, such an experiment would be unreasonably biased if it were to ask
for volunteers to make up its groups. Random assignment makes it equally likely that any
participant will be placed in any group.
RANDOM SAMPLE- A random sample is a sample that is selected completely by
chance from the population.
REPRESENTATIVE SAMPLE- A representative sample is one in which the relevant
characteristics of the sample members are generally the same as the characteristics of the
population.
SAMPLE- A sample is a part of the population examined in a study to gain information
about the whole population. For example, if the population is a third grade class with 30
students, the sample of 5 would be surveyed to represent the population.
SAMPLE SIZE- The sample size is the number of observations taken from a population
to form a sample. For example, when 5 students are interviewed regarding the time they
spend on homework, the size of this sample is 5. Increasing the sample size generally
leads to estimates that are more accurate.
COMPARATIVE STUDY- A comparative study focuses on the relationship(s) between
two or more sets of data. For example, a comparative study might demonstrate that, on
average, the students will spend more time doing homework and reading during the
school year that during summer vacation or weekends. Comparative studies often use box
plots and other statistical comparisons to prove that the distributions are different in a
significant way.
CENSUS- A census is an attempt to include every individual in a given population in a
sample.
WORK CITED
Albert B. Bennett Jr., Laurie J. Burton, L. Ted Nelson. Mathematics for Elementary
Teachers. An Active Approach. Seventh edition. McGraw-Hill. New York NY
2007
WWW.DOE.MASS.EDU/FRAMEWORKS/MATH
WWW.LEARNER.COM
WWW.NCES.ED.GOV