Transcript Collecting and Analyzing Data - EDUN322

Collecting, Organizing, and
Interpreting Data
Chapter Sixteen
Test Grades
Stem Leaf
4
2
5
6
7
7
3 8
8
2 4 6
9
1 4 9
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Elementary school research model
1.
2.
3.
4.
5.
6.
7.
Brainstorm for questions that children would like
answered.
Choose one of the questions or problems.
Predict what the outcome will be.
Develop a plan to test the predicted outcome.
Carry out the plan.
Analyze the data. Is the hypothesis supported?
Look back. Answer the question. Should the
information be shared? With whom? How could it
be shared?
(Bohan, Irby, & Vogel, 1995)
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Concrete
Stage
Concrete
–
Pictorial
Stage
Pictorial
–
Abstract
Stage
Abstract
Stage
The level of graphing experience is not determined by
the chosen topic but the way the data are presented.
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www.icanteachmychild.com/2010/
07/early-graphing-activity/
 Early graphing experiences should involve
constructing graphs with concrete materials.
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 Involves using both pictorial representations of
objects and concrete materials.
 Children are able to compare more than two events.
 A one-to-one correspondence between the object or
picture and what is being graphed is still present.
www.kindergartenlessons.com/graphingactivities.html
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 Bar Graphs
 Pictures or objects are used to represent an item on the
graph.
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www.athens.edu
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 Children continue making bar graphs with pictures but
are now beginning to use abstract objects to form the
graph.
www.brainpopjr.com/
 Pictographs
 Used to read, interpret, and
discuss results through questioning
Trees planted on Earth Day
http://www.livebinders.com/play/play?i
d=69022
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 One-to-one correspondence of objects has been
replaced with a one-to-many correspondence.
 Rectangular bars can replace colored squares in a bar
graph
 Pictographs can be used with the objects representing
many different things
www.eduplace.com
crayola.com
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 One-to-one correspondence of objects has been
replaced with a one-to-many correspondence.
 Line graphs can be introduced
 Data
points are joined with a line
http://vickimartinez.c
om/math_gc_unit3.ht
ml#Line
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Maximum and Minimum Temperatures for 1 Year
100
80
Degrees Fahrenheit
60
40
20
0
-20
-40
Jan
Feb
Mar
Apr
May
June
July
Aug
Sept
Oct
Nov
Dec
Maximum
2
16
22
48
56
62
78
80
62
56
40
20
Minimum
-18
0
10
18
40
44
56
46
38
24
16
-6
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 Shows how the whole is broken into parts.
 Steps to help children construct a circle graph:
1. Collect the data and calculate the total.
2. Calculate the fractional part each data piece is of the total.
3. Express each fraction as a percent.
4. Calculate the number of degrees out of 360° that each fractional
part represents.
5. Draw the graph, using the degrees from step 4 to determine the
size of each sector.
6. Label the graph and each sector.
www.themathlab.com
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www.ck12.org/
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 Histograms – a graphical representation of the
frequency with which scores occur
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 Line Plots – uses a symbol, such as an X, to
indicate the frequency of each data point
http://www.eduplace.com/
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 Stem-and-Leaf Plots
 Method of showing the frequency that data occurs
 Stem – part of the data that shows the beginning
value
 Leaf – next digit to the right of the stem
Complete a stem-and-leaf plot for the following list of grades
on a recent test:
73, 42, 67, 78, 99, 84, 91, 82, 86, 94
I'll use the tens digits as the stem values and the ones digits
as the leaves.
42, 67, 73, 78, 82, 84, 86, 91, 94, 99
Since I know where these data points came from
("a recent test"), I'll use a title. Then my plot looks like this:
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Test Grades
Stem Leaf
4
2
5
6
7
7
3 8
8
2 4 6
9
1 4 9
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 Five reasons to include statistics and probability in the
school mathematics program:
1.
2.
3.
4.
5.
They provide meaningful applications of mathematics at all
levels.
They provide methods for dealing with uncertainty.
They give us some understanding of the statistical
arguments, good and bad, with which we are continually
bombarded.
They help consumers distinguish sound use of statistical
procedures from unsound or deceptive uses.
They are inherently interesting, exciting, and motivating
topics for most children.
(Shulte & Smith, 1981, p. ix)
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 Descriptive statistics refers to the collection,
organization, presentation, and interpretation of
data.
 Frequency
 Measures of Central Tendency
 Mode – most frequently occurring value in a set of data
Prices of 10 Ice Cream Specialties sold at Ben & Jerry’s
STEM LEAF
9
0
10
005
11
05
12
0005
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Mode = $1.20
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 Measures of Central Tendency
 Median – the middle number in a set of data
 100, 100, 99, 98, 92, 91, 91, 90, 88, 87, 87, 85, 85, 85,80,
79, 76,72, 67,66, 45
 Median is 87
 Mean – the average of the set of data
American History Test
Marco
90 ..... Adriane
Linda
75 ..... Christy
Chantelle 88 ..... Jay
Ralph
68 ..... Marcus
Chi Bo
92 ..... Donnie
Class mean is 82.4
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85
99
45
97
85
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 A plot that shows the summary of data and provides a
visual representation of the variability within the data.
 Requires five values
 Median = 80
 Upper quartile = 95
 Lower quartile = 66
 Upper extreme = 100
 Lower extreme = 45
Averages of Math class: 45, 55, 66, 66, 70, 80, 88, 90, 95, 98, 100
45
66
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50 55 60 65
80
70
75 80 85
16-19
95
100
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90 95 100
 Probability is the analysis of the chance of
something occurring.
P(event) = Number of Desired Favorable Outcomes
Number of Total Possible Outcomes
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1. Probability is a measure of the likelihood of
future events.
2. A sample space is a set of all possible
outcomes and their associated probabilities of
occurring.
3. Probability helps predict outcomes of simple
experiments.
4. Students can make estimates of probability by
using data from experiments.
(Tarr, 2002)
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 Informal and nonnumeric probability activities should
help children think about concepts such as:
 Certain – Class of 30 girls. Teacher picks 1 child.
Certain to pick a girl.
 Impossible – Spinner has no purple. Impossible to spin
and land on purple.
 Equally likely – Spinner has 4 colors. Equally likely
to land on any color.
 More likely – More likely to land on red or blue
 Less likely – Less likely to land on yellow or green
 Activities should include
 Prediction
 Experimentation
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 Children should begin
 Using conventional probability terms
 Assigning probability values to some events
 Experimental probability - based on the outcomes of
an experiment
 Theoretical probability – based on mathematical
formula
P(event) = Number of Desired Favorable Outcomes
Number of Total Possible Outcomes
 Engaging in simple simulations
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 Probability activities at this level should
include:
 An emphasis on determining theoretical values
 Experimental probability
 Advanced work with simulating events

The Game of SKUNK
 http://illuminations.nctm.org/LessonDetail.aspx?id=L248
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