Chapters 1 & 3
Graphical Methods for
Describing Data
Mr. Potter
•
•
•
•
•
•
•
•
•
•
Bachelors in Mathematics w/ Education
Masters in Educational Leadership
Doctoral Student, Psych of Cog/Instruction
World Champion in Taekwondo
Married 16 years, my son Kai is 13 in 8th
grade at McMillan, my daughter Kaitlin is 4
Turn in information sheet
Tutoring times
Electronics – no phones, no music - Calc’s
Dress code – if I tell you to tuck, it will be
documented
Tardies
• Prerequisites – successful completion of
Algebra 2 or above
• Homework
• Supplies
– TI-84 or TI-83 plus calculator – preferred is TI-84
• AP Exam
– Thursday, May 12, 2016 – 12:00 pm
– Test:
• 40 Multiple choice questions
• 5 free response questions
• 1 investigative task
– What is the passing rate?
What is statistics?
• the science of collecting,
organizing, analyzing, and
drawing conclusions from data
Why should one study
statistics? Can dogs help
patients with heart
1. To be informedfailure
...
by reducing
a) Extract information stress
from tables,
andcharts
and graphs
anxiety?
b) Follow numerical arguments
c) Understand the basics
of how
data should
When
people
take
be gathered, summarized, and analyzed to
a
vacation
do
they
draw statistical conclusions
really leave work
behind?
Why should one study
statistics? (continued)
Many companies now require drug
2.screening
To makeasinformed
judgments
a condition
of employment.
With these screening tests there is a
risk of a false-positive reading. Is the
If you choose a particular major, what
risk of a false result acceptable?
are your chances of finding a job when
you graduate?
3. To evaluate decisions that affect
your life
What is variability?
Suppose you went into a convenience
In fact,
variability
is
store
toquality,
purchase
a soft
drink.universal!
Does
The
state,
oralmost
degree
of
being
every can variable
on the shelf
contain exactly 12
or changeable.
ounces?
It is variability that makes
life interesting!!
NO – there may be a little more or less in
the various cans due to the variability
that is inherent in the filling process.
If the Shoe Fits ...
The two histograms to
the right display the
distribution of heights
of gymnasts and the
distribution of heights
of female basketball
players. Which is
which? Why?
Heights – Figure A
Heights – Figure B
If the Shoe Fits ...
Suppose you found a pair of size 6 shoes
left outside the locker room. Which team
would you go to first to find the owner of
the shoes? Why?
Suppose a tall woman (5 ft 11 in) tells you
see is looking for her sister who is
practicing with a gym. To which team
would you send her? Why?
The Data Analysis Process
1. Understand the nature of the problem
It is important
to haveand
a clear
2. Decide
what to measure
how to
It
is important
select and
apply
measure
itbeforetogathering
direction
data.
appropriate
inferential statistical
3.Itthe
Collect
data
is important to
carefully define the
methods
This
often
leads
to develop
the
variables
tostep
be studied
and to
It is
important
to understand
how
4. formulation
Summarize of
data
and
performquestions.
new
research
appropriate
methods
for determining
data
is collected
because
the type of
preliminary
analysis
their
values.
analysis that
is appropriate
depends
5. Perform formal analysis
This
analysis
provides
insight
on initial
how the
data was
collected!
into important characteristics of the
6. Interpret results
data.
Suppose we wanted to know the
average GPA of high school
graduates in the nation this year.
We could collect data from all
high schools in the nation.
What term would be used to describe
“all high school graduates”?
Population
• The entire collection of
individuals or objects about which
information is desired
What
do
you
call
it
when
you
• A census is performed to gather
collect
data
about
the
entire
about the entire population
population?
GPA Continued:
Suppose we wanted to know the
average GPA of high school
graduates
in
the
nation
this
year.
Why might we not want to use a
census here?
We could collect data from all
high schools in the nation.
If we didn’t perform a census,
what would we do?
Sample
• A subset of the population, selected
for study in some prescribed manner
What would a sample of all high school
graduates across the nation look like?
High school graduates from each state
(region), ethnicity, gender, etc.
GPA Continued:
Suppose we wanted to know the
Once we have collected the data,
average GPA of high school
what would we do with it?
graduates in the nation this year.
We could collect data from a sample
of high schools in the nation.
Descriptive statistics
• the methods of organizing &
summarizing data
If the sample of high school GPAs contained
1,000 numbers, how could the data be organized
or summarized?
• Create a graph
• State the range of GPAs
• Calculate the average GPA
GPA Continued:
Suppose we wanted to know the
average GPA of high school graduates
in the nation this year.
We could collect data from a sample
Could
we
use
the
data
from
our
of high schools in the nation.
sample to answer this question?
Inferential statistics
• involves making generalizations from
a sample to a population
Based on the sample, if the average GPA for high
school graduates was 3.0, what generalization
could be made?
The average national GPA for this year’s
high school graduate is approximately 3.0.
Could someone claim that the average GPA for
graduates
in your
school district
is 3.0?
Be sure
tolocal
sample
from the
No. Generalizations based on the results of a
sample can only be made back to the population
from which the sample came from.
population of interest!!
Variable
• any characteristic whose value may
change from one individual to
another
• Suppose we wanted to know the
IsGPA
thisofa high
variable
. . .
average
school
The number
ofnation
wrecks
peryear.
week
graduates
in the
this
Define
of interest.
at the
the variable
intersection
outside
The variable of school?
interest isYES
the
GPA of high school graduates
Data
• The values for a variable from
individual observations
For this variable . . .
The number of wrecks per week at the
intersection outside . . . What could
observations be?
0, 1, 2, …
Two types of variables
categorical
numerical
discrete
continuous
Categorical variables
• Qualitative
• Identifies basic differentiating
characteristics of the population
Can you name any categorical
variables?
Numerical variables
• quantitative
• observations or measurements take
on numerical values
• makes
to average
these values
Cansense
you name
any numerical
variables?
• two types - discrete & continuous
Discrete (numerical)
• Isolated points along a number line
• usually counts of items
Continuous (numerical)
• Variable that can be any value in a
given interval
• usually measurements of something
Identify the following variables:
1. the color of cars in the teacher’s lot
Categorical
2. the number of calculators owned by
students at your school Discrete numerical
3. the zip code of an individual
Is money a measurement orCategorical
a count?
4. the amount of time it takes students to
drive to school
Continuous numerical
5. the appraised value of homes in your city
discrete numerical
Classifying variables by the
number of variables in a data set
Suppose that the PE coach records the
height of each student in his class.
This is an example of a
univariate data
Univariate - data that describes a single
characteristic of the population
Classifying variables by the
number of variables in a data set
Suppose that the PE coach records the
height and weight of each student in his
class.
This is an example of a
bivariate data
Bivariate - data that describes two
characteristics of the population
Classifying variables by the
number of variables in a data set
Suppose that the PE coach records the
height, weight, number of sit-ups, and
number of push-ups for each student in
his class.
This is an example of a
multivariate data
Multivariate - data that describes more than
two characteristics (beyond the scope of this
course)
Graphs for categorical
data
Bar Chart
When to Use
Categorical data
How to construct
– Draw a horizontal line; write the categories
or labels below the line at regularly spaced
intervals
– Draw a vertical line; label the scale using
frequency or relative frequency
– Place equal-width rectangular bars above
each category label with a height determined
by its frequency or relative frequency
Bar Chart (continued)
What to Look For
Frequently or infrequently occurring
categories
Collect the following data and then display the data in a
bar chart:
What is your favorite ice cream flavor?
Vanilla, chocolate, strawberry,
or other
Double Bar Charts
When to Use
Categorical data
How to construct
– Constructed like bar charts, but with two (or
more) groups being compared
– MUST use relative frequencies on the
vertical axis
– MUST include a key to denote the different
Whybars
MUST we use relative frequencies?
Each year the Princeton Review conducts a
survey of students applying to college and of
parents of college applicants. In 2009, 12,715
high school students responded to the question
“Ideally how far from home would you like the
college you attend to be?” Also, 3007 parents
of students applying to college responded to
the question
“how
far from
would you like
What
should
you home
do first?
the college your child attends to be?” Data is
displayed in the frequency table below.
Frequency
Ideal Distance
Students
Parents
Less than 250 miles
4450
1594
250 to 500 miles
3942
902
500 to 1000 miles
2416
331
More than 1000 miles
1907
180
Create a
comparative
bar chart
with these
data.
Relative Frequency
Ideal Distance
Students
Parents
Less than 250 miles
.35
.53
250 to 500 miles
.31
.30
500 to 1000 miles
.19
.11
More than 1000 miles
.15
.06
Found
Foundby
bydividing
dividingthe
thefrequency
frequencyby
bythe
thetotal
total
number
numberofofstudents
parents
What does this
graph show about
the ideal distance
college should be
from home?
Segmented (or Stacked) Bar
Charts
When to Use
Categorical data
How to construct
– MUST first calculate relative frequencies
– Draw a bar representing 100% of the group
– Divide the bar into segments corresponding
to the relative frequencies of the categories
Remember the Princeton survey . . .
Create a segmented bar graph with these
data.
Relative Frequency
First
Ideal Distance
Students
Less than 250 miles
.35
250 to 500 miles
.31
500 to 1000 miles
.19
More than 1000 miles
.15
draw a
Parents bar that
.53
represents
.30 100% of the
.11
students who
.06
answered the
survey.
Relative Frequency
Relative frequency
Notice
Ideal Distance
that this
segmented
Students
Parents bar chart
Less
than 250 miles
.35 relationship
.53
displays
the same
between the
250
to 500 miles
.31
opinions
of students
and .30
parents concerning
500
to 1000
miles
.19 that college
.11
the
ideal
distance
is from home
More than 1000
.15
as miles
the double
bar .06
chart does.
First
draw
a
1.0
Next,
divide
Do the
same
thing
bar
that
themiles
bar into
Less than 250
0.8
for
parents –
represents
250 to 500 miles
segments.
don’t
forget
a
key
0.6
100%
of
the
500 to 1000 miles
denoting
each
More than
1000 miles who
students
0.4
category
answered
the
0.2
survey.
Students
Parents
Pie (Circle) Chart
When to Use
Categorical data
How to construct
– Draw a circle to represent the entire data set
– Calculate the size of each “slice”:
Relative frequency × 360°
– Using a protractor, mark off each slice
To describe
– comment on which category had the largest
proportion or smallest proportion
Typos on a résumé do not make a very good
impression when applying for a job. Senior
executives were asked how many typos in a
résumé would make them not consider a job
candidate. The resulting data are summarized
in the table below.
Number of Typos
Frequency Relative Frequency
1
60
.40
2
54
.36
3
21
.14
4 or more
10
.07
Don’t know
5
.03
Create a pie
chart for
these data.
Number of Typos
1
2
Frequency Relative Frequency
What does this
pie chart
tell us about the
60
.40
number of54typos occurring
in résumés
.36
21 applicant
.14 would not be
before the
4 or more
10
.07
considered
for
a job?
3
Don’t know
5
.03
First draw a
Next,
calculate
circle
to each
Repeat
for
the
size
ofthe
the
represent
slice.
slice
for “1
typo”
entire
data
set.is the
Here
.40×360º
=144º
completed
pie
chart created
Draw
slice.
usingthat
Minitab.
Graphs for numerical
data
Dotplot
When to Use
Small numerical data
sets
How to construct
– Draw a horizontal line and mark it with an
appropriate numerical scale
– Locate each value in the data set along the scale
and represent it by a dot. If there are two are
more observations with the same value, stack the
dots vertically
Dotplot (continued)
What to Look For
–
–
–
–
The representative or typical value
The extent to which the data values spread out
The nature of the distribution along the number line
The presence of unusual values
Collect the following data and then display the data in a dotplot:
How many body piercings do you
have?
How to describe a
numerical, univariate
graph
What strikes you as the most distinctive
difference among the distributions of
exam scores in classes A, B, & C ?
1. Center
• discuss where the middle of the
data falls
• three measures of central tendency
– mean, median, & mode
The mean and/or median is typically
reported rather than the mode.
What strikes you as the most distinctive
difference among the distributions of
scores in classes D, E, & F?
2. Spread
• discuss how spread out the data is
• refers to the variability in the data
Remember,
Standard deviation
& IQR will be discussed
in Chapter
Range = maximum
value – 4
minimum value
• Measure of spread are
– Range, standard deviation, IQR
What strikes you as the most distinctive
difference among the distributions of
exam scores in classes G, H, & I ?
3. Shape
• refers to the overall shape of the
distribution
The following slides will discuss these
shapes.
Symmetrical
1. Collect data by rolling two dice and
recording the sum of the two dice.
• refers
datatimes.
in which both sides
Repeatto
three
are (more or less) the same when
the
graph
is folded
2.
Plot
your sums
on thevertically
dotplot ondown
the
board.
the
middle
• bell-shaped is a special type
3. What shape does this distribution
–have?
has a center mound with two
sloping tails
Uniform
1. Collect data by rolling a single die and
recording the number rolled. Repeat
• refers
to data in which every class
five times.
has equal or approximately equal
frequency
2.
Plot your numbers on the dotplot on
To
help
remember
the
board.
the name for this
shape, picture
3.soldier
What shape
does
standing
in this distribution
have?
straight lines.
What are they
wearing?
Skewed
1. Collect data finding the age of five
coins in circulation (current year
Name
a variable
distribution
minus
year ofwith
coin)aand
record that is
skewed
left.one side
• refers to data
in which
(tail)
longer
than
other
side
2.
Plot is
the
ages on
thethe
dotplot
on the
board.
• the direction of skewness is on the
3.
What
shape
does
this
distribution
side of the longer tail
have?
The directions are right skewed or left
skewed.
Bimodal (multi-modal)
Suppose collect data on the time it
takes totodrive
San of
Luis
Obispo,
• refers
the from
number
peaks
in
California
California.
the
shapeto
ofMonterey,
the distribution
Some people may take the inland
• Bimodal
would have two
peakswhile
route (approximately
2.5 hours)
others may take
thehave
coastal
route
• Multi-modal
would
more
than
(between 3.5 and 4 hours).
two peaks
Bimodal
distributions can occur when the
data set consist of observations from
What
shape would
thisofdistribution
two different
kinds
individuals or
Whathave?
would a distribution be called if it
objects.
had ONLY one peak?
Unimodal
3. Shape
• refers to the overall shape of the
distribution
• symmetrical, uniform, skewed, or
bimodal
What strikes you as the most distinctive
difference among the distributions of
exam scores in class J ?
4. Unusual occurrences
• Outlier - value that lies away from
the rest of the data
• Gaps
• Clusters
5. In context
• You must write your answer in
reference to the context in the
problem, using correct statistical
vocabulary and using complete
sentences!
Dotplot (continued)
What to Look For
–
–
–
–
The representative or typical value
The extent to which the data values spread out
Describealong
thethedistribution
The nature of the distribution
number line
the number of body
The presence of unusual values
of
piercings the class has.
Collect the following data and then display the data in a dotplot:
How many body piercings do you
have?
Numerical Graphs
Continued
Stem-and-Leaf Displays
When to Use
Univariate numerical data
How to construct
Each
is
split
into
two
parts:
Can
also number
create
comparative
stem-and-leaf
– Select
one
or more
of the
leading
digits
for the
Remember
collected in Chapter 1 – how many
stem the data setdisplays
piercings
do–you
have? stem
Would
a stem-and-leaf
display
be a
– List
the
possible
in
a
vertical
column
Stem
consists
of values
the
first
digit(s)
Use
for
small
to
good
graph
for
this
distribution?
Why
or
why
not?
–Leaf
Record
the leaf forof
each
observation
beside
consists
the
final
digit(s)
each corresponding stem valuemoderate sized
data
sets.
– Indicate the units for stems andBe
leaves
in to
a key
sure
list
or legend
Doesn’t
work
well
If you have
a long
lists
of
every
stem
from
for
leaves behind
asmallest
fewdata
stems,
thelarge
to
To describe
sets.
you can split
in value
order
thestems
largest
– comment on the center, spread, and shape of the
spread
the
distribution and if there aretoany
unusualout
features
distribution.
The following data are price per ounce for
various brands of different brands of dandruff
shampoo at a local grocery store.
0.32 0.21 0.29 0.54 0.17 0.28 0.36 0.23
Create a stem-and-leaf display with this data?
What
would
an
List
the
stems
For
the
observation
of
Stem Leaf
TheContinue
median
price
per
ounce
recording
each
appropriate
stem
Describe
this
vertically
“0.32”,
write
the
2 is
7
1
for dandruff
shampoo
leaf with
the
be?
distribution.
behind
the
“3”
stem.
$0.285,
with
a
range
corresponding
stemof
2
1 9 8 3
$0.37. The distribution is
2 6
3
positively skewed with an
4
outlier at $0.54.
5
4
The Census Bureau projects the median age in 2030 for
the 50 states and Washington D.C. A stem-and-leaf
display is shown below.
Notice
now you
We use L for lower leaf
valuesthat
(0-4)
see(5-9).
the shape of
and H for higher leaf can
values
this distribution.
Notice that you really cannot
We can split the stems in order
see a distinctive shape for this
to better see the shape of the
distribution due to the long list
distribution.
of leaves
The median percentage of primary-school-aged
The following
is
data
on the
percentage
ofto thein
children
enrolled
inCreate
school
is
larger
for
countries
Let’s
truncate
the
leaves
a to
comparative
stemBe
sure
use
comparative
What
is
an
appropriate
primary-school-aged
who
are enrolled
in
Northern Africa thanchildren
in
Central
Africa,
but
the
unit
place.
and-leaf
display. these
language
when
describing
stem?
schoolare
forthe
19 countries
in distribution
Northern Africa
and
ranges
same. The
for countries
distributions!
for
23
countries
in
Central
in Northern Africa is strongly
negatively“4”
skewed, but
“4.6” African.
becomes
the distribution for countries in Central Africa is
approximately symmetrical.
Northern Africa
54.6 34.3 48.9 77.8 59.6 88.5 97.4 92.5 83.9
98.8 91.6 97.8 96.1 92.2 94.9 98.6 86.6 96.9
88.9
Central Africa
58.3 34.6 35.5 45.4 38.6 63.8 53.9 61.9 69.9
43.0 85.0 63.4 58.4 61.9 40.9 73.9 34.8 74.4
97.4 61.0 66.7 79.6
Histograms
When to Use
Univariate numerical data
How to construct
DiscreteConstructed
data
For comparative
histograms
– use
―Draw
a horizontal scale
and mark
it with
thefor
possible
differently
values
for the variable
two separate
graphs with
the same
discrete
versus
―Draw
a on
vertical
scale
and mark
it with frequency
continuous
data or
scale
the
horizontal
axis
relative frequency
―Above each possible value, draw a rectangle centered
at that value with a height corresponding to its
frequency or relative frequency
To describe
– comment on the center, spread, and shape of the
distribution and if there are any unusual features
Queen honey bees mate shortly after they
become adults. During a mating flight, the queen
usually takes several partners, collecting sperm
that she will store and use throughout the rest of
her life. A study on honey bees provided the
following data on the number of partners for 30
queen bees.
12
8
9
2
3
7
4
5
5
6
6
4
6
7
7
7
10
4
8
1
6
7
9
7
8
7
8
11
6
10
Create a histogram for the number of partners of
the queen bees.
7
6
5
4
3
2
1
0
0
1
2
3
4
5
6
7
8
9
10
11
12
Draw a
First draw a
rectangle
Next
draw a
horizontal
above
each
vertical
axis, scaled
value
with
a
axis,
scaled
with the
height
with
possible
corresponding
frequency
values
of
to
the
or
relative
the variable
frequency.
offrequency.
interest.
Suppose we use relative frequency
instead of frequency on the vertical
What do you notice about the shapes
axis.
of these two histograms?
Histograms
When to Use
Univariate numerical data
How to construct
Continuous data
―Mark the boundaries of the class intervals on the
horizontal axis
―Draw a vertical scale and mark it with frequency or
relative frequency
―Draw
a rectangle
directly
above each class
This
is the type
of histogram
that interval
withmost
a height
corresponding
to its frequency
students
are familiar
with. or
relative frequency
To describe
– comment on the center, spread, and shape of the
distribution and if there are any unusual features
A study examined the length of hours spent
The median
number
ofahours
spent
watching
watching
TV per
day for
sample
of children
TV per day was greater for the 1-year-olds
age
1
and
for
a
sample
of
children
age
3.
Below
than for the 3-year-olds. The distribution for
are the
comparative
histograms.
3-year-olds
was more strongly skewed
right than the distribution for the 1-year-olds,
Notice
the
common
scaleranges.
on
but the two
distributions
had
similar
Write
a few
sentences
the horizontal
axis
comparing
the distributions.
Children Age 1
Children Age 3
Cumulative Relative Frequency Plot
When to use
- used to answer questions about percentiles.
How to constructPercentiles are a value with a
given of
percent
of observations
- Mark the boundaries
the intervals
on the
at or below that value.
horizontal axis
- Draw a vertical scale and mark it with relative
frequency
- Plot the point corresponding to the upper end of
each interval with its cumulative relative
frequency, including the beginning point
- Connect the points.
The National Climatic Center has been collecting
the
cumulative
weatherFind
data for
many
years. The relative
annual rainfall
amounts for Albuquerque,
New
Mexico
from 1950 to
frequency
for
each
2008 were used to create
the frequency distribution
interval
below.
Annual Rainfall
(in inches)
Relative
frequency
4 to <5
0.052
5 to <6
0.103
6 to <7
0.086
7 to <8
0.103
8 to <9
0.172
9 to <10
0.069
10 to < 11
0.207
11 to <12
0.103
12 to <13
0.052
13 to <14
0.052
Cumulative relative
frequency
+
+
0.052
0.155
0.241
Continue this
pattern to
complete the
table
The National Climatic Center has been collecting
weather
data for
many years.relative
The annual
rainfall
To create
a cumulative
frequency
amounts
Albuquerque,
Newthe
Mexico
from
1950of
to
plot,for
graph
a point for
upper
value
2008the
were
used to and
create
frequency distribution
interval
thethe
cumulative
relative
In the context offrequency
this
below.
Annualexplain
Rainfall the
Relative
problem,
frequency
(in inches)
meaning of this value.
Cumulative relative
frequency
4 to <5
0.052
0.052
5 to <6
0.103
0.155
6 to <7value one0.086
0.241
Why isn’t this
Plot
a point for
each interval.
7(1)?
to <8
0.103
0.344
8 to <9
0.516
Plot
aofstarting
point at (4,0).
In the context
this 0.172
to <10
0.069 points. 0.585
Connect
problem, 9explain
the the
10 to < 11
0.207
0.792
meaning of this value.
11 to <12
0.103
0.895
12 to <13
0.052
0.947
13 to <14
0.052
0.999
Cumulative relative frequency
1.0
0.8
0.6
What proportion of years had
rainfall amounts that were
9.5 inches or less?
Approximately 0.55
0.4
0.2
2
4
6
8
Rainfall
10
12
14
Cumulative relative frequency
1.0
0.8
Approximately 30% of the years
had annual rainfall less than
what amount?
0.6
0.4
0.2
Approximately 7.5 inches
2
4
6
8
Rainfall
10
12
14
Which interval of
rainfall amounts
had a larger
proportion of years
–
9 to 10 inches or
10 to 11 inches?
Explain
Cumulative relative frequency
1.0
0.8
0.6
The interval 10 to 11
inches, because its slope
is steeper, indicating a
larger proportion
occurred.
0.4
0.2
2
4
6
8
Rainfall
10
12
14
Displaying Bivariate
Numerical Data
Scatterplots
When to Use
Bivariate numerical data
Scatterplots are
How to construct discussed in much
greater
depth
in
- Draw a horizontal scale
and mark
it with
Chapter
5. variable
appropriate values of the
independent
- Draw a vertical scale and mark it appropriate
values of the dependent variable
- Plot each point corresponding to the
observations
To describe
- comment the relationship between the variables
Time Series Plots
When to Use
- measurements collected over time at regular
intervals
How to construct
Can abe
considered
- Draw
horizontal
scale and mark it with
bivariate
data
where
the
appropriate
values
of time
y-variable
is thescale
variable
- Draw a vertical
and mark it appropriate
values
of the
observed
measured
and
the x-variable
- Plotvariable
each point
corresponding to the
is time
observations and connect
To describe
- comment on any trends or patterns over time
The accompanying time-series plot of movie box
office totals (in millions of dollars) over 18
weeks in the summer for 2001 and 2002
appeared in USA Today (September 3, 2002).
Describe any
trends or
patterns
that you see.
Who, What, When, Where,
Why, How
• Who?
– Individual cases about whom we record some
characteristics. Individuals who answer a survey are
called respondents. People on whom we experiment are
subjects or participants but animals, plants, and other
inanimate subjects are called experimental units.
• What and why?
– Type of variable and why you need to look at this variable.
• Where, When, and How?
– What methods were used to collect the data?
– Where and when addresses differences in years and
locations which may be important.
Context
• Context – The context tells Who was
measured, How the data were collected,
where the data were collected, and When
and Why the study was performed.
• Every question must be
answered in context in
complete sentences.