2. Objectives
• Define Frequency Distribution
• Identify the Parts of the Frequency Table
• Organize data using Frequency Distribution
• Represent data in Frequency Distribution
graphically using Histograms, Frequency
Polygons and Ogives
3. Introduction
Statistics is of vital importance in vast
variety of fields. It's obvious that society
can’t be run effectively on the basis of
hunches or trial and error, and that in
business and economics much depend on
the correct analysis of numerical
information. Decisions based on data will
provide better results than those based on
intuition or gut feelings.
4. Introduction
Statistical thinking permeates all social
interaction. For example, take these
questions:
• ‘Which university should I go to?’
• ‘Should I buy a new car or a second-hand
one?’
5. Introduction
• ‘Should the company buy this building or
just rent it?’
• ‘Should we invest now or wait till the new
financial year?’
• ‘When should we launch our new product?’
6. Introduction
All of these require decisions to be
made, all have costs and benefits, all are
based upon different amounts of data, and
all involve or necessitate some kind of
statistical calculation. This is where an
understanding of statistics and knowledge of
statistical techniques will come in handy.
7. Frequency
Distributions
Frequency Distribution is the basic
building block of statistical analytical
methods and the first step in analyzing
survey data. It helps researchers organize
and summarize the survey data in a
tabular format, interpret the data and
detect extreme values in the survey data
set.
8. Frequency
Distributions
• When data are collected in original form,
they are called Raw Data.
• When the raw data is organized in table
form, using classes and frequencies, it
becomes Statistical Data using Frequency
Distribution functions.
• When raw data is organized into frequency
tables it now becomes Information.
10. Types of
Frequency Distributions
• Categorical Frequency Distributions
- can be used for data that can be
placed in specific categories, such
as nominal- or ordinal-level data.
• Examples - political affiliation,
religious affiliation, blood type etc.
12. Ungrouped
Frequency Distributions
• Ungrouped Frequency Distributions
- can be used for data that can be
enumerated and when the range of
values in the data set is not large.
• Examples - number of miles your
instructors have to travel from home
to campus, number of girls in a 4-
child family etc.
13. Number of Miles Travelled
Example
Class Frequency
5 24
10 16
15 10
14. Grouped
Frequency Distributions
• Grouped Frequency Distributions -
can be used when the range of
values in the data set is very large.
The data must be grouped into
classes that are more than one unit
in width.
• Examples - the life of boat batteries
in hours.
15. Lifetimes of Boat Batteries
Example
Class
limits
Class
Boundaries
Cumulative
24 - 37 23.5 - 37.5 4 4
38 - 51 37.5 - 51.5 14 18
52 - 65 51.5 - 65.5 7 25
frequency
Frequency
16. Parts of Frequency Table
• Class Limits groupings or categories
defined by lower and upper limits
• Lower Class Limits are the smallest
numbers that belongs to the different
classes.
• Upper Class Limits are the highest
numbers that belongs to the different
classes.
17. Lifetimes of Boat Batteries
Frequency Table
• Class Limits represent the smallest and
largest data values that can be included
in a class.
• In the lifetimes of boat batteries
example, the values 24 and 37 of the
first class are the class limits.
• The lower class limit is 24 and the upper
class limit is 37.
18. Lifetimes of Boat Batteries
Frequency Table
Class Limits Frequency
24-37 4
38-51 14
52-65 7
Lower Class
Limits
19. Lifetimes of Boat Batteries
Frequency Table
Class Limits Frequency
24-37 4
38-51 14
52-65 7
Upper Class
Limits
20. Parts of Frequency Table
• The class boundaries are used to
separate the classes so that there are
no gaps in the frequency distribution.
21. Class Boundaries
• Steps to calculate class boundaries:
1. Subtract the upper class limit for the first
class from the lower class limit for the
second class.
38-37 = 1
2. Divide the result by two.
1÷2 = 0.5
22. Terms Associated
with a Grouped
Frequency Distribution
3. Subtract the result from the lower class
limit and add the result to the upper class
limit for each class.
Class Limits Class
Boundaries
Frequency
24-37 23.5-37.5 4
38-51 37.5-51.5 14
52-65 51.5-65.5 7
23. Parts of Frequency table
• The class midpoint a point that divides a
class into two equal parts. This is the
average of the upper and lower class limits.
Class Limits Midpoint Frequency
24-37 30.5 4
38-51 44.5 14
52-65 58.5 7
24. Parts of Frequency Table
• The class width for a class in a frequency
distribution is found by subtracting the lower
(or upper) class limit of one class minus the
lower (or upper) class limit of the previous
class.
Class Limits Frequency
14 24-37 4
14 38-51 14
14 52-65 7
Class Width
27. Types of Frequency
Distribution
• Cumulative Frequency Distribution is used
to determine how many or what
proportion of the data values are below or
above a certain value.
• To create a cumulative frequency polygon,
scale the upper limit of each class along
the x-axis and corresponding cumulative
frequency along the y-axis
29. Guidelines for Constructing
a Frequency Distribution
• There should be between 5 and 20
classes.
• The class width should be an odd
number.
• The classes must be mutually
exclusive.
30. Guidelines for Constructing
a Frequency Distribution
• The classes must be continuous.
• The classes must be exhaustive.
• The class must be equal in width.
31. Procedure for
Constructing a Grouped
Frequency Distribution
• Find the highest and lowest value.
• Find the range.
• Find the number of classes by using
k= 1+3.322log N. Round-up your
answers.
• Find the width by dividing the range by
the number of classes and rounding
up.
32. Procedure for
Constructing a Grouped
Frequency Distribution
• Select a starting point (usually the
lowest value); add the width to get the
lower limits.
• Find the upper class limits.
• Find the boundaries.
• Tally the data, find the frequencies and
find the cumulative frequency.
33. Grouped
Frequency Distribution
Example
• In a survey of 20 patients who smoked,
the following data were obtained. Each
value represents the number of cigarettes
the patient smoked per day. Construct a
frequency distribution using six classes.
(The data is given on the next slide.)
34. 10 8 6 14
22 13 17 19
11 9 18 14
13 12 15 15
5 11 16 11
Grouped
Frequency Distribution
Example
35. Grouped
Frequency Distribution
Example
• Step 1: Find the highest and lowest
values: H = 22 and L = 5.
• Step 2: Find the range:
R = H – L = 22 – 5 = 17.
• Step 3: Select the number of classes
desired. In this case it is
equal to 6.
37. • Step 5: Select a starting point for the
lowest class limit. For convenience,
this value is chosen to be 5, the
smallest data value. The lower class
limits will be 5, 8, 11, 14, 17 and 20.
Grouped
Frequency Distribution
Example
38. • Step 6: The upper class limits will
be 7, 10, 13, 16, 19 and 22. For
example, the upper limit for the first
class is computed as 8 - 1, etc.
Grouped
Frequency Distribution
Example
39. • Step 7: Find the class boundaries
by subtracting 0.5 from each lower
class limit and adding 0.5 to the
upper class limit.
Grouped
Frequency Distribution
Example
40. • Step 8: Tally the data, write the
numerical values for the tallies in the
frequency column and find the
cumulative frequencies.
• The grouped frequency distribution is
shown on the next slide.
Grouped
Frequency Distribution
Example
41. Class Limits Class Boundaries Frequency Cumulative Frequency
05 to 07 4.5 - 7.5 2 2
08 to 10 7.5 - 10.5 3 5
11 to 13 10.5 - 13.5 6 11
14 to 16 13.5 - 16.5 5 16
17 to 19 16.5 - 19.5 3 19
20 to 22 19.5 - 22.5 1 20
Note: The dash “-” represents “to”.
42. Visualizing Data
• The three most commonly used
graphs in research are:
• The histogram.
• The frequency polygon.
• The cumulative frequency graph, or
ogive (pronounced o-jive).
43. Visualizing Data
• The histogram is a graph that
displays the data by using vertical
bars of various heights to represent
the frequencies.
45. Visualizing Data
• A frequency polygon is a graph that
displays the data by using lines that
connect points plotted for
frequencies at the midpoint of
classes. The frequencies represent
the heights of the midpoints.
47. Visualizing Data
• A cumulative frequency graph or
ogive is a graph that represents the
cumulative frequencies for the
classes in a frequency distribution.
51. Pie Graph
• Pie graph - A pie graph is a circle
that is divided into sections or
wedges according to the percentage
of frequencies in each category of
the distribution.
52. Pie Graph
Robbery (29, 12.1%)
Rape (34, 14.2%)
Assaults
(164, 68.3%)
Homicide
(13, 5.4%)
Pie Chart of the
Number of Crimes
Investigated by
Law Enforcement
Officers In U.S.
National Parks
During 1995
53. Summary
In this discussion, we present the difference
between raw data and frequency distribution that
sometimes gives us confusion. We also show how
data can be group for easier analysis. There we
have categorical frequency distribution,
ungrouped frequency distribution and the most
challenging among the three the grouped
frequency distribution.
54. Summary
After grouping the data, frequency polygon,
histogram, ogive and other graphical techniques
are used to present them in an effective and
memorable way.
Gathered facts or data are not enough in
measuring reliability for a certain research. Thus,
tabular or graphical representations make visual
comparison of data easier and give a more lasting
impression than is possible by any other means.
55. Assessment
• Outpatient wait time: Waiting times (minutes) for 25
patients at a public health clinic are:
35 22 63 6 49 19 16 31
24 29 23 32 72 13 51 45
77 16 33 55 10 42 28 72
13
• Create a frequency distribution table with frequency,
relative/percent frequencies, cumulative frequencies.
Construct a histogram, frequency polygon and ogive.
56. “Statistics can be made to prove
anything – even the truth.”
– Anonymous
57. Group 4
FRANZ GELECA C. CARRANZA
BERNADETTE MONTILLA
JOAN J. PRINCIPE
BERVERLY BARRUN
RUBY JHANE FLORES
MARIE SEDICOL
DOMINGO ESPARES JR.
JOHN MARK RECTO
THANK YOU.
