In this lesson we enrich what the students have already learned from Grade 1 to 10 about presenting data. Additional concepts could help the students to appropriately describe further the data set.

1. DATA
PRESENTATION
Let’s appropriately
describe and present the
data set

2. Learning Outcomes
At the end of the lesson, the learner is able
to
identify and use the appropriate method
of presenting information from a data set
effectively.

3. Textual or Narrative, Tabular and
Graphical Method of Presentation

4. TEXTUAL/PARAGRAPH/NARRATIVE
FORM
• One describes the data by enumerating
some of the highlights of the data set like
giving the highest, lowest or the average
values.
• In case there are only few observations,
say less than ten observations, the values
could be enumerated if there is a need to
do so.

5. Example
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)

6. TABULAR
• applicable for large data sets.
• Trends could easily be seen in this
kind of presentation.
• However, there is a loss of information
when using such kind of presentation.
• The frequency distribution table is the
usual tabular form of presenting the
distribution of the data.

7. COMMON PARTS OF STATISTICAL TABLE
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.

8. •a table should have at least three
rows and/or three columns.
•too many information to convey
in a table is also not advisable.
•Tables are usually used in written
technical reports and in oral
presentation.

10. GRAPHICAL PRESENTATION
• a visual presentation of the data.
• commonly used in oral presentation.
• There are several forms of graphs to use like the
pie chart, pictograph, bar graph, line graph,
histogram and box-plot. Which form to use
depends on what information is to be relayed. For
example, trends across time are easily seen using a
line graph.
• However, values of variables in nominal or ordinal
levels of measurement should not be presented
using line graph. Rather a bar graph is more
appropriate to use.

17. The FDT
• An FDT is a presentation containing
non-overlapping categories or classes of
a variable and the frequencies or counts
of the observations falling into the
categories or classes. There are two
types of FDT according to the type of
data being organized: a qualitative FDT
or a quantitative FDT.

18. Two Types of FDT according to the
type of data being organized:
1. Qualitative FDT
• the non-overlapping categories of the
variable are identified, and frequencies, as
well as the percentages of observations
falling into the categories, are computed.
2. Quantitative FDT
• two types: ungrouped and grouped FDT.

19. Qualitative Data FDT (example)

20. Qualitative Data Bar graph
(example)

21. Two Types of Quantitative 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. The distinct
values are grouped into class intervals.

22. Example
55 70 57 73 55 59 64 72
60 48 58 54 69 51 63 78
75 64 65 57 71 78 76 62
49 66 62 76 61 63 63 76
52 76 71 61 53 56 67 71

23. Steps in the construction of a grouped
FDT
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 𝑘 = 𝑁,
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.

24. 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
1
10 𝑥 ,
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.

25. 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 (if needed) the following 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)

26. 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)

27. 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.

29. The histogram is a graphical presentation of the
frequency distribution table in the form of a
vertical bar graph. There are several forms of the
histogram and the most common form has the
frequency on its vertical axis while the true class
boundaries in the horizontal axis.
As an example, the FDT and its corresponding
histogram of the 2012 estimated poverty
incidences of 144 municipalities and cities of
Region VIII are shown

31. Key Points
• Three methods of data presentation: textual,
tabular and graphical
• Two or all the methods could be combined to
fully describe the data at hand.
• Distribution of data is presented using frequency
distribution table and histogram.