Watching cartoons was one of our favorite
past-times back when we were still kids.
Are you familiar with the TV cartoon
shown on the given picture below?
statistics for the rest of Lesson 1 up until
Lesson 3.
After going through this module, the
students will be able to:
1. Distinguish
between
descriptive
statistics
and
inferential
statistics,
population
and
sample,
parameter and statistic, and
constant and variable.
For those who are familiar with the
cartoon, we all know that it is centered on
the rivalry between the two titular
characters Tom and Jerry. As a kid who
watched the TV show, how did you find
your experience?
Due to the rivalry between Tom and
Jerry, we would constantly see them
fighting over something that sometimes
would lead to violence. Because of this,
articles were written blaming the TV
cartoon or recommending not to watch it
due to the violence it depicts. This leads us
to the question:
Does watching violence on TV affect a
child’s behavior?
In order to answer this question, a
research must be done. We will need to
gather
information
regarding
the
children’s behavior and the TV programs
they watched. Then out of the data we
gathered, we analyze it then interpret the
result- which are exactly what statistics
do.
Module 1 introduces us to statistics and
its role in research. We have three lessons
in this module. Lesson 1 begins with the
definition of statistics and a brief
discussion of the role of statistics in
research. We then introduce the
fundamental terms and concepts we use in
2. Distinguish and characterize
the three different commonly
used research designs in any
research endeavors.
3. Classify
variables
as
quantitative or qualitative,
independent or dependent, and
discrete or continuous and
classify measurements as
nominal, ordinal, interval or
ratio.
Lesson 1: Statistics and Research
So what is statistics? Is this the same as
those we hear from beauty pageants when
the host give us the vital statistics of each
contestants?
The term statistics can mean different
in a lot of ways. However, the term
statistics that we use here refer to the
shortened version of statistical procedures.
What are these?
Definition
1.1
Statistical
procedures consist
of
formulas,
calculations, and procedures used for
organizing, summarizing, and interpreting
information [1, 2].
So it is statistics that gives sense out
of the data we gather from a survey or
research. Research on behavioral sciences
use statistics to explain the results of the
research and to provide evidence whether
to support or debunk a certain theory.
So how does research and statistics
work together?
A research always starts with a general
question regarding a certain group. These
groups can be a group of people, animals,
corporations, parts produced in a factory,
or anything that a researcher wants to
study. Say for example we want to conduct
a study that claims “the more you study
statistics, the better you’ll learn them.” So
who do we subject to this study? This is
what we need to figure out first.
Definition 1.2 A population refers to the
entire group that a researcher wishes to
study
[1].
The size of the population can vary. It
can be extremely large or very small. When
the population is extremely large, is it
possible to examine all of the individuals
belonging in the population? No, it would
take forever. So what do we do instead? In
this case, researchers typically select a
smaller group from the population to
subject to their study which we call
a sample.
Definition 1.3 A sample is a relatively
smaller group taken from the population
that is intended to represent the
population. The individuals measured in a
sample
are
called participants or subjects [2].
Now the population and the sample
depends on your perspective. Say for
example we want to study the amount of
learning the students in your statistics
class obtained. If we are only interested in
the students in your class, then they
already constitute the population.
However, if we are interested in all college
students studying statistics, then they
constitute the population and the sample
can be the students in your statistics class.
Note that the sample is meant to be a
representative of the population. In other
words, we assume that the participants
from the sample behaves the same way as
the individuals we find in the population.
So the results we get out of the sample of
the students in your statistics class is used
to conclude that we will get the same result
from the population of all college students.
After identifying the population and
the sample to observe, the next thing we
need to consider is to define the specific
situation and behaviors we want to
observe and measure from the population
or sample. Say for example, we might be
interested in the influence of the amount of
time one studies to its scores in the major
exam. As the amount of study time
changes, do the scores in the quiz also
change? In this case, we are referring to
the variables.
Definition
1.4 A variable is
a
characteristic or a condition that differs
from one participant to another.
A variable can be the any
characteristics of an individual such as age,
height, weight, gender, personality, or
intelligence. It can also be environmental
conditions that change such as
temperature or time of day.
To show the changes, we need to
measure the variables being examined.
The measurement we obtain from each
participant is called a datum, or
commonly, a score or a raw score. The
complete set of scores is called the data
set or simply the data [1].
Now to make a distinction whether the
data come from a population or a sample,
we use the term parameter to refer to the
characteristic describing a population
while statistic is used to refer to a
characteristic describing a sample. For
example, the average score from the
population is a parameter while the
average score from the sample is a
statistic. The research process usually
begins with a question regarding the
population parameter. When we select a
sample from the population to examine,
the actual data come from the sample
which we then use to compute the sample
statistics. It is important to note that for
every population parameter, there is
always a corresponding sample statistic.
Definition
1.6
Inferential
statistics consist of techniques that allow
us to study samples and then make
generalizations about the populations
from which they were selected [1].
However, in reality, it is unlikely that
the sample statistics are identical to the
population parameters. Say for example
we have a population of 500 USJ-R college
students taking up a Statistics course. We
take two sections of any of the Statistics
class with 40 students each as our sample.
The population parameters and sample
statistics obtained are provided below.
Descriptive and Inferential Statistics
Now, statistics has two divisions
namely descriptive and inferential
statistics.
In descriptive statistics, we take raw
scores and organize or summarize them by
plotting a table or drawing a graph, or by
taking the average of the scores. In this
case, even if we have hundreds of scores
from our data, the average only provides a
single descriptive value for the entire data.
Definition 1.5 Descriptive statistics are
statistical procedures used to summarize,
organize, and simplify data [1].
On the other hand, inferential statistics
analyzes the results taken from the sample
in order to make a general statement about
the population. This is done by using the
sample statistics to draw conclusions
about population parameters since the
sample is assumed to represent the
population.
Do you see the difference in the
statistics between the two samples? Do
you see the difference between the sample
statistics and the population parameters?
In reality, we cannot expect the sample
to give the exact same results we have of
the whole population because there is
always some discrepancy between the
sample statistics and the population
parameter. This discrepancy is what we
call as the sampling error.
Definition 1.7 Sampling error is the
naturally occurring discrepancy, or error,
that exists between a sample statistic and
the population parameter [1].
However this discrepancy may not
necessarily mean that there is a significant
difference between the two groups. The
difference might be due to chance. This is
what we need to examine through
inferential statistics. The role of inferential
statistics is to interpret the results. From
the table above, we see a difference of 12.4
in the average IQ of the two samples. This
leads us to formulate two interpretations.
two variables. This can be done using two
methods.
Measuring two variables for each participant:
The correlational Method
This method is done by simply measuring
the two variables for each participant.
Let’s consider the same scenario, say we
want to examine if a relationship exists
between the number of hours a college
student studies to the result of his/her
exam. We use a survey to measure the
amount of study time and the class record
to measure the exam result for each
participant. The table below shows an
example of the data gathered in the study.
Student
Study time
(in hours)
A
B
C
D
E
F
G
H
I
J
3
1
5
4
3
4
4
3
5
2
1. There is no real difference
between the average IQ of the
students, and the 12.4-point
difference between the two
samples is just an example of
sampling error.
2. There really is a difference
between the average IQ of the
students, and the 12.4-point
difference between the two
samples was not due to chance.
The problem for inferential statistics is to
differentiate the two interpretations.
Lesson 2: Research and Statistical Methods
Most of the time, the goal of a research is to
study the relationship between two or more
variables. For example, is there a relationship
between the number of hours of study time
and the results of the exam of college
students? To determine whether a
relationship exists or not, we measure the
Exam Score
(in
percentage)
81
68
98
95
78
91
87
69
100
75
We then look if consistent patterns
exist in the data in order to provide
evidence that a relationship exists
between the two variables- as the amount
of study time changes from one student to
another, is there also a tendency for the
exam result to change? Consistent patterns
in the data can easily be seen if we plot the
scores in a graph such as the one below.
Comparing Two (or more) Groups of Scores:
Experimental and non-Experimental Methods
In comparing two or more groups of
scores for a study, the following research
design can be used.
Definition 2.2 Experimental Method is a
research design that can establish a
cause
Do you see a relationship between the
study time and the exam results?
A research study that simply measures
two different variables for each individual
is an example of the correlational method,
or the correlational research strategy.
Definition
2.1 In
the correlational
method, two different variables are
observed to determine whether there is a
relationship between them [1].
Although the correlational method can
show the existence of a relationship
between two variables, it cannot give an
explanation, in particular, of a cause-andeffect relationship. From our given
example, we see that a systematic
relationship exists between the study time
and the exam results for a group of college
students; those who study more tend to
have better exam results. However, there
are many possible explanations for this
relationship to exist. To demonstrate a
cause-and-effect relationship between two
variables, we use the experimental method
instead.
and effect relationship between two
variables. The method of observing
variables is intended to show that changes
in one variable are caused by changes in
the other variable. That is, one variable is
manipulated while changes are observed
in another variable.
The variables that are studied in the
experimental
method
consist
of
the independent
and dependent variables.
The independent variable is the variable
manipulated by the researcher. This
variable usually consists of two or more
treatment conditions to which subjects are
exposed. On the other hand, the dependent
variable is a variable that is observed to
asses a possible effect of the manipulation
of the independent variable. Moreover,
there other experiments that will include a
condition wherein the subjects do not
receive any treatment known as the
controlled condition and a condition
where the subject do receive the
experimental treatment called the
experimental condition.
For example, consider the data from
an experimental study examining the
relationship between temperature and
eating
behavior.
The
researcher
manipulated temperature to create three
treatment conditions and then measured
eating behavior for a sample of 5 rats in
each of the three conditions.
scores for a group of males versus a group
of females.
Definition 2.5: A time variable simply
involves comparing individuals at
different points in time.
For instance, a researcher may
measure depression before therapy and
then measure it again after therapy.
The situation below considers a
study that uses a quasi-experimental
research design.
Definition 2.3 The Quasi – Experimental
Method is a research design that deals
with research studies that are almost, but
not quite, real experiments. This research
design uses a non-manipulated variable to
define the conditions that are being
compared. The non-manipulated variable
is usually subject variable (i.e. male versus
female) or time variable, such as before
treatment and after treatment. The nonmanipulated variable that assumes or
defines the conditions is called a quasiindependent variable.
Example: An example of data from a quasi
– experimental study examining the
relationship between IQ and attitude
toward school. The researcher used IQ to
define three groups of students and then
measured attitude toward school for the
five students in each group. The resulting
attitude toward school for the five
students in each different group in terms
of IQ levels are shown below.
The following are definitions of
subject and time variables and its usage
in a sample situations of research
endeavors.
Definition 2.4 A subject variable is a
characteristic such as age or gender
that varies from one subject to
another.
For example, a researcher might
want to compare communication skills
Lesson 3: Variables and measurements
The study or assessment in a
psychology field generally make use of
variables. The variables can be the any
characteristics of an individual such as age,
height, weight, gender, personality, or
intelligence. It can also be environmental
conditions that change such as
temperature or time of a day.
These variables are generally
classified
as qualitative or quantitative variables.
A qualitative variable is a variable that
yields categorical responses. For instance,
gender variable has male or female
categorical responses. An economic status
as a variable can assume values such as
low, middle, or upper class categorical
responses.
On
the
other
hand,
a quantitative variable is a variable that
yields numerical responses representing
an amount or quantity. For example,
income, IQ scores, expenditures, study
time, etc. are variables that assumes or
yields numerical responses.
Quantitative variables are further
characterize as discrete or continuous
variables.
A discrete
quantitative
variable consists of separate, indivisible
categories. This type of variable contains
no intermediate values between two
adjacent categories. For example, when we
roll a die, the possible outcome that may
appear as a result is either a 1, 2, 3, 4, 5, or
6. Observe that in between neighboring
values, no other values can ever be
observed, that is, the values always pertain
to a whole number. The response values
for discrete quantitative variables can also
be obtained through the process counting.
For instance, to get the response value for
the variable, number of students in a
psychological statistics 1 class, one can
employ a counting process, using a natural
or counting numbers. Further examples of
discrete quantitative variables are income,
IQ, expenditures, exam scores, age, etc.
On the other hand, continuous
quantitative variables are variables that
have infinite number of possible values
that fall between any two observed values.
It is divisible into an infinite number of
fractional parts. For instance, suppose a
researcher is measuring heights for a
group of individuals participating in a
certain study. Since height is a continuous
quantitative variable, it can be viewed as a
continuous line. Observe that there are an
infinite number of possible points on the
line without any gaps between
neighboring
values.
Furthermore,
continuous quantitative variables yield
responses that can be obtained through
the process of measurements with
corresponding units of measurements.
The following are some examples of
continuous variables whose responses can
be obtained through the process of
measurements with corresponding units.
1.
2.
3.
4.
5.
Height
Time
Temperature
Weight
Volume
Types of Variables according to their level of
measurement
In a study or assessment in a
psychology field, the data collection
requires that we make measurements of
our observations. Measurement involves
assigning individuals or events to
categories. The categories can simply be
names such as male/female or
favorable/unfavorable, or they can be
numerical values such as 36 degrees
Celsius or 45 degrees Celsius. The
categories used to measure a variable
make up a scale of measurement, and the
relationships between the categories
determine different types of scales.
Remark: The distinctions among
the
scales are important since they identify the
limitations
of
certain
types
of
measurements and because certain
statistical treatments are appropriate for
scores that have been measured on some
scales but not on others.
For instance, if you were interested
in individual’s weight, you could measure
a group of individuals by simply classifying
them into two categories: light and heavy.
However, this typical classification would
not tell us much about the actual weights
of the individuals, and hence, these
measurements would not give us sufficient
information to calculate an average weight
for the group. Although the above simple
classification would be enough for some
purposes, we would need more
sophisticated measurements before one
could answer more detailed questions or
research questions of interest.
In this lesson, we examine and
characterize variables according to their
levels of measurement.
student would be classified in a category
according to his or her preference.
Remark: The measurements from a
nominal scale can be used to determine
whether two individuals are different,
however, they do not identify either the
direction or the size of the difference.
For instance, if one student chooses
to prefer on a subject schedule and
another, is not preferred for the schedule,
then, we can say that they are different,
but we cannot say that being preferred is
“more than” or “less than” not being
preferred and hence, we cannot specify
how much difference there is between
preferred and not preferred categories.
Definition 1: A nominal scale consists of
a set of categories that have different
names. Measurements on a nominal scale
label and categorize observations, but do
not make any quantitative distinctions
between observations.
Remark: Although a nominal scale
categories are not quantitative values,
they are occasionally represented by
numbers.
A. Nominal Scale
The word nominal means “having
to do with names.” The scale of
measurement on a nominal scale involves
classifying individuals into categories that
have different names but are not
connected to each other in any way.
For example, if you were measuring
the preference for a group of psychology
college students for a subject time
schedule, the categories would be
preferred or not preferred. Then each
Example: Cell phone numbers can be
used to identify the owners or the rooms
or offices in a building may be identified by
numbers. Observe that cell phone
numbers or room or office numbers are
simply names and do not reflect any
quantitative information.
The following are further examples
of variables with nominal scale of
measurements.
1. Marital Status
2. Gender
3. Ethnicity
4. Racial Origin
5. Civil Status
6. Card Number
7. Occupation and so on
B. The ordinal scale
An ordinal scale also have different
names as its categories as in a nominal
scale. However, the categories can be
organized
in
a
fixed
order
corresponding to differences of
magnitude.
Definition
2: An ordinal
scale involves a set of categories that
are organized into an ordered
sequence. That is, measurement on an
ordinal scale involves ranking
observations or categories.
Examples:
1. Working Performance can be
categorized and ranked as follows:
1 - Best Worker
2 - Second Best Worker
3 – Third Best
Worker
and So on
2. Academic Performance can
be categorized and
ordered as follows:
4 – Excellent
3 – Very Satisfactory
2 – Satisfactory
1
–
Needs
Improvement
3. Service Satisfaction
Ranked Categories:
Very Unsatisfied
Fairly Unsatisfied
Neutral
Fairly Satisfied
Very Satisfied
4. Socioeconomic class
Upper Class
Middle Class
Lower Class
Remark: Ordinal scales are often used
to measure variables for which it is
difficult to assign numerical scores. For
instance, an individual can rank their
song preferences but might have
problem explaining “how much” they
prefer rock songs than love songs.
C. Interval Scale
The interval scale consists of an
ordered set of categories (like an
ordinal scale) with the additional
requirement that the categories form a
series of intervals that are all exactly
the same size. The distances between
any two numbers are known which are
numeric in nature and does not have a
stable starting point or absolute
zero. That is, a value of zero does not
indicate a total absence of the variable
being measured.
For example, a temperature of 0°
Celsius does not mean that there is no
temperature, and it does not prohibit
the temperature from going even
lower.
The following are further examples of
variables with interval scale of
measurements.
Examples: Fahrenheit, IQ Scores,
Personality
Test,
Scholastic
Achievement Test, Calendar Time
(Gregorian, Hebrew, or Islamic), Etc..
D. Ratio Scale
Ratio Scale are also an interval
scale with the additional feature of an
absolute zero point. That is, a zero point is
not arbitrary and has a meaningful value
representing none or a complete absence
of the variable being measured. The
existence of an absolute, non arbitrary
zero point implies that we can measure the
absolute amount of the variable; that is, we
can measure the distance from 0. Thus, it
is possible to compare measurements in
terms of ratios.
For example, an individual who
needs 60 minutes to solve a puzzle has
taken twice
as much time as an individual who
finishes in only 30 minutes.
Remark: Using a ratio scale, we can
measure the direction and the size of the
difference between two measurements
and describe the difference in terms of a
ratio.
The following are further examples
of variables with ratio scale of
measurements.
1.
2.
3.
4.
Height
Weight
Reaction Time
Number of Errors on a Test
Module 2: Organization and Presentation of Data
Introduction
In conducting a behavioral research or
assessment, one must gather data for the
variable/s under investigation. In order to
describe situations, create conclusions or
making inferences about the occurrence of
events, one must organize the data
gathered in a more meaningful
manner. Once the data is organized, the
next move that one can do is to present the
data so that those who will be benefited
directly or indirectly from reading the
study or assessment can understand
it. The most commonly used procedure of
presenting data is through using graphs
and charts. Each of these graphs and
charts has its specific functions depending
on the nature of the variables being
investigated.
Module 2 discusses on how to
organize data by constructing frequency
distribution and the manner the data will
be presented by constructing graphs and
charts.
After going through this module, the
students will be able to:
1. Discuss and explain the methods in
organizing and presenting data.
2. Organize the data into a frequency
distribution using excel data
analysis.
3. Represents frequency distribution
graphically using histogram,
frequency polygons, and
cumulative frequency polygon
(ogives).
4. Plot the data using bar graph
(multiple bar graph), pie chart,
time series graph and scatter plot.
5. Analyse and interpret the
Cla
ss
graphs/charts in the context of the
variable/s under investigation.
6. Show volunteerism and
innovativeness in organizing and
presenting data concerning real
life behavioural application
problems.
Lesson 1: constructing the Frequency
Distribution Table
A grouped frequency distribution is useful
whenever the range of the data set is quiet
large. Hence, the data must be grouped into
classes whether it is categorical or interval or
ratio data. The following shows the procedure
for constructing the frequency distribution.
A. Categorical Frequency Distribution
The categorical frequency distribution
is utilized to organize nominal or
ordinal type of data. For instance, we
can employ categorical frequency
distribution for variables such as
gender, marital status, socio-economic
status, political affiliation and so on.
Example: Twenty
psychological
statistics students were given an
academic performance evaluation by
their instructor. The data set is shown
as follows:
Average
High
Low
Average
Low
High
Low
High
High
Average
High
Average
Low
High
Average
High
Low
Average
Average
Average
The following shows the categorical
frequency distribution for the data.
T
a
ll
y
||
||
|
||
||
|||
|
||
||
|||
Lo
w
Av
era
ge
Hig
h
Freq
uenc
y
Pe
rce
nt
5
25
8
40
7
35
Remark: The percentage is computed
using the formula:
%=f/n x 100, where f=frequency of the
class and n is the total number of
categorical values.
Learning Check
Construct the frequency distribution for
the data on Job Satisfaction by rank and
file employees of a certain company.
Slightly
Satisfied
Satisfied
Quite
Satisfied
Satisfied
Very
Satisfied
Satisfied
Quite
Satisfied
Satisfied
Slightly
Satisfied
Satisfied
Very Satisfied
Quite Satisfied
Satisfied
Slightly satisfied
Satisfied
Quite Satisfied
Slightly
Quite
Slightly
Very
Quite
Satisfied
Very Satisfied
Very
Quite
Satisfied
Quite Satisfied
Slightly
Quite
B. The Frequency Distribution for
numerical data (Interval or Ratio data)
Data in its original form and
structure are called raw data.
Example: The following is a raw data
depicting the number of students taking
the IQ test during a year in 60 randomly
selected classes in a certain university.
60 – 69
Components
of
Distribution Table
1
15
a
Frequency
The following are the components of a
Frequency Distribution Table
I. Class Interval
These are the numbers defining the
class. It consist of the end numbers called
the class limits namely the lower limit and
upper limit.
II. Class Frequency (f)
This component shows the number
of observations falling in the class.
When these scores are arranged in
either
ascending
or
descending
magnitude, then such an arrangement is
called an array. It is usually helpful to put
the raw data in an array because it is easy
to identify the extreme values or the values
where the scores most cluster. When the
data are placed into a system wherein they
are organized, then these partake the
nature of grouped data.
Definition: The
procedure
of
organizing data into groups is called a
Frequency Distribution Table (FDT)
Example: The following presents a
frequency distribution table of the exam
scores of fifteen Behavioral Students.
Scores
Frequenc
y
20 – 29
30 – 39
40 – 49
50 – 59
5
4
3
2
III. Class Boundaries
These are the so called “true class
limits”. They are classified as:
Lower Class Boundary (LCB), which is
defined as the middle value of the lower
class limits of the class and the upper class
limit of the preceding class and Upper
Class Boundary that is, the middle value
between the upper class limit of the class
and the lower limit of the next class.
IV. Class Size
The difference between
consecutive upper limits or
consecutive lower limits.
two
two
V. Class Mark (CM)
This component is the midpoint or
the middle value of a class interval.
VI. Cumulative frequency (CF)
This component shows the
accumulated frequencies of successive
classes.
There are two types of Cumulative
Frequencies.
A. Greater than CF (> CF) – shows the
number of observations greater than the
lower class boundary (LCB).
B. Less than CF (< CF) - shows the number
of observations less than the upper class
boundary (UCB).
In constructing a Frequency
Distribution Table, attention must be
given in selecting the number of class
intervals or groupings in the table. There
are no exact rules for determining this
number of class intervals. However, one
suggestion in literature for determining
the number of class intervals is to use
Sturges’ rule such as the one specified in
Step 1.
1. Determine the number of classes. For
first approximation, it is suggested to use
the Sturge’s Approximation Formula.
K= 1 + 3.332 log n
where K = approximate number of
classes
n = number of cases
2. Determine the range R, where R =
maximum value – minimum value
3. Determine the approximate class size C
using the formula
C = R / K. It is usually convenient to
round off C to a nearest whole number
4. Determine the lowest class interval (or
the first class). This class should include
the minimum value in the data set. For
uniformity, let us agree that for our
purposes, the lower limit of the class
interval should start at the minimum
value.
5. Determine all class limits by adding the
class size C to the limits of the previous
class.
6. Tally the scores / observations falling in
each class.
Example: Construct
a
Frequency
Distribution Table for the number of
students taking the IQ test during a year in
60 randomly selected classes in a certain
university
Solution:
1. Using the Sturge’s Approximation
Formula, K=
1
+
3.332
log n, where K,
approximate
number of classes and n, number
of cases, then the approximated
number of class intervals for the
data set is given by
K= 1 + 3.332 log(60)
=
1 + 3.332(1.77815125)
K=
6.92 or 7
2. The range R is given by
27 –
32
33 –
38
39 –
44
45 –
50
51 –
56
57 –
62
Total
R=Maximum ValueMinimum Value
=59 – 21
= 38
3. The approximate class size C is:
C=R/K
=38/7
=5.43
or 6
4. The lowest class interval (or the
first class) is 21 – 26.
11
28.33
18.33
4
35.00
6.67
6
45.00
10.00
9
60.00
15.00
17
88.33
28.33
7
100.00
11.67
n=60
100.
00
Thus,
the Complete
Frequency
Distribution Table is as follows:
5. Adding the class size C=6 to the
class limit beginning with the
lowest class interval, we then
obtain the other class intervals
shown as follows:
Class
Intervals
21 – 26
27 – 32
33 – 38
39 – 44
45 – 50
51 –
56
57 - 62
6. Tally of Scores and the Frequency
Distribution Table
Class
Inter
val
21 –
26
Freque
ncy
6
Cumula
tive
Percent
10.00
Perc
ent
10.00
Clas
s
Inte
rval
21 –
26
27 –
32
33 –
38
39 –
44
45 –
50
51 –
56
57 –
62
Tota
l
Frequ
ency
6
11
4
6
9
17
7
n=60
Class
Bound
aries
20.5 –
26.5
26.5 –
32.5
32.5 –
37.5
38.5 –
44.5
44.5 –
50.5
50.5 –
56.5
56.5 –
62.5
Cla
ss
Ma
rk
23.
5
29.
5
35.
5
41.
5
47.
5
53.
5
59.
5
Cumulat
ive
Frequen
cy
Gre Le
ater ss
than th
CF an
(>
CF
CF) (<
CF
)
60
6
54
17
43
21
39
27
33
36
24
53
7
60
Note: Data analysis found in excel can be
used to generate the frequency
distribution once the class intervals are
already set. Just use histogram function
under data analysis window as shown
below. For the bin range, the upper class
limits of each class intervals is being used.
For the input range, enter the range of
occupied cells of data defined by the
variable number of students taking the IQ
test. Then, enter the range of upper class
limits into the bin range. Consequently,
check levels, cumulative percentage, chart
output and click ok.
Excel Output
Bin Range
26
32
38
44
50
56
62
More
Frequency
6
11
4
6
9
17
7
0
Cumulative %
10.00%
28.33%
35.00%
45.00%
60.00%
88.33%
100.00%
100.00%
Learning Check 2
A research study has been
conducted examining the number of
children in the families living in a certain
community. The following data has been
collected based on a random sample of n =
40 families from the community.
2, 2, 5, 3, 0, 1, 3, 2, 3, 4, 1, 3, 4, 5, 7, 3, 2, 4,
1, 0, 5, 8, 6, 5, 4 , 2, 4, 4, 7, 6, 3, 5, 5, 2, 2, 1,
1, 3, 4, 6. Organize this data in a Frequency
Distribution Table.