Statistics and probability lesson5

Lesson 5 – Data Presentation
Ms. Maria Christita Polinag
Miriam College Adult Education

Textual or Narrative Presentation:
 Detailed information are given in textual
presentation
 Narrative report is a way to present data.
- one describes the data by enumerating some
of the highlights of the data set:
 highest, lowest or the average values

 The country’s poverty incidence among
families as reported by the Philippine Statistics
Authority (PSA), the agency mandated to
release official poverty statistics, decreases
from 21% in 2006 down to 19.7% in 2012. For
2012, the regional estimates released by PSA
indicate that the Autonomous Region of
Muslim Mindanao (ARMM) is the poorest region
with poverty incidence among families
estimated at 48.7%. The region with the
smallest estimated poverty incidence among
families at 2.6% is the National Capital Region
(NCR).

Tabular Presentation:
 Numerical values are presented using tables.
 Information are lost in tabular presentation of
data.
 Frequency distribution table is also applicable
for qualitative variables
- applicable for large data sets
- should have at least three rows and/or three
columns

a. Table title includes the number and a
short description of what is found inside
the table.
b. Column header provides the label of what
is being presented in a column.
c. Row header provides the label of what is
being presented in a row.
d. Body are the information in the cell
intersecting the row and the column.

Graphical Presentation:
 Trends are easily seen in graphs compared to
tables.
 It is good to present data using pictures or
figures like the pictograph.
 Pie charts are used to present data as part of
one whole.
 Line graphs are for time-series data.
 It is better to present data using graphs than
tables as they are much better to look at.

- a visual presentation of the data
- commonly used in oral presentation
Several forms of graphs:
a. Pie
b. Chart
c. Pictograph
d. Bar graph - values of variables in nominal or
ordinal levels
e. Line graph - trends across time are easily seen
f. Histogram
g. Box-plot

 A special type of tabular and graphical
presentation
 Used to depict the distribution of the data
 Most of the time, these are used in technical
reports
FDT - a presentation containing non-
overlapping categories or classes of a variable
- the frequencies or counts of the observations
falling into the categories or classes

1. Qualitative FDT
- the non-overlapping categories of the
variable are identified and frequencies
- the percentages of observations falling into
the categories are computed
2. Quantitative FDT
- two types: ungrouped and grouped FDT

1. Ungrouped FDT - is constructed when there
are only a few observations or if the data set
contains only few possible values
2. Grouped FDT - is constructed when there is
a large number of observations and when
the data set involves many possible values
- distinct values are grouped into class
intervals

1. Identify the largest data value or
the maximum (MAX) and smallest
data value or the minimum (MIN)
from the data set and compute
the range, R. The range is the
difference between the largest
and smallest value,
i.e. R = MAX – MIN.

2. Determine the number of classes,
k using , where N is the
total number of observations in the
data set. Round-off k to the nearest
whole number. It should be noted
that the computed k might not be
equal to the actual number of
classes constructed in an FDT.

3. Calculate the class size, c, using
c = R/k. Round off c to the
nearest value with precision the
same as that with the raw data.

4. Construct the classes or the class intervals.
A class interval is defined by a lower limit (LL) and an
upper limit (UL).
The LL of the lowest class is usually the MIN of the
data set.
The LL’s of the succeeding classes are then obtained
by adding c to the LL of the preceding classes.
The UL of the lowest class is obtained by subtracting
one unit of measure , where x is the maximum
number of decimal places observed from the raw
data) from the LL of the next class.
The UL’s of the succeeding classes are then obtained
by adding c to the UL of the preceding classes.
The lowest class should contain the MIN, while the
highest class should contain the MAX.

5. Tally the data into the classes
constructed in Step 4 to obtain the
frequency of each class. Each
observation must fall in one and
only one class.
6. Add distributional characteristics.

a. True Class Boundaries (TCB).
The TCBs reflect the continuous
property of a continuous data.
It is defined by a lower TCB (LTCB) and
an upper TCB (UTCB).
These are obtained by taking the
midpoints of the gaps between
classes or by using the following
formulas:
LTCB = LL – 0.5(one unit of measure)
and
UTCB = UL + 0.5(one unit of measure).

b. Class Mark (CM).
The CM is the midpoint of a class and is
obtained by taking the average of the
lower and upper TCB’s,
i.e. CM = (LTCB + UTCB)/2

c. Relative Frequency (RF).
The RF refers to the frequency of the
class as a fraction of the total
frequency,
i.e. RF = frequency/N
RF can be computed for both qualitative
and quantitative data.
RF can also be expressed in percent.

d. Cumulative Frequency (CF).
The CF refers to the total number of
observations greater than or equal to
the LL of the class (>CF) or the total
number of observations less than or
equal to the UL of the class (<CF).

e. Relative Cumulative Frequency (RCF).
RCF refers to the fraction of the total
number of observations greater than
or equal to the LL of the class (>RCF)
or the fraction of the total number of
observations less than or equal to the
UL of the class (<RCF).
Both the <RCF and>RCF can also be
expressed in percent.

- is a graphical presentation of the
frequency distribution table in the
form of a vertical bar graph.
frequency - vertical axis
true class boundaries - horizontal axis.

 TEACHING GUIDE FOR SENIOR HIGH SCHOOL - Statistics
and Probability by CHED in collaboration with the
Philippine Normal University

Statistics and probability lesson5

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