Data presentation for senior high school

3. DESCRIPTIVE STATISTICS
- enable us to understand data through summary values and graphical
presentations.
- can be illustrated in an understandable fashion by presenting them graphically
using statistical and data presentation tools.
A. TABULAR PRESENTATION OF DATA
Tables display numbers or words arranged in a grid. Tabular method can be used
to represent data sets with two variables.
A tabular presentation is illustrated in Table 1.

4. Table 1
Profile of the Respondents in Terms of Age and Gender
Age Bracket
Male Female
F % F %
21-25 9 8.18 4 3.63
26-30 8 7.27 14 12.72
31-35 7 6.36 6 5.45
36-40 6 5.45 7 6.36
41-45 9 8.18 22 20
46-50 5 4.54 8 7.27
51-Above 2 1.81 3 2.72
Total 46 41.79% 64 58.15%
Frequency Table
Purpose. Frequency or one-way tables represent the simplest method for analyzing categorical
(nominal) data.

5. For example, in a survey of spectator interest in different sports, we could summarize the
respondents’ interest in watching basketball in a frequency table as follows.
“Watching Basketball”
Response Frequency Cumulative
f
Percentage Cumulative
Percent
Always
Oftentimes
Sometimes
Seldom
Never
39
16
26
19
0
39
55
81
100
0
39.00
16.00
26.00
19.00
0
39.00
55.00
81.00
100
0
The table above shows the number, proportion, and cumulative proportion of
respondents who characterized their interest in watching basketball as (5) Always
interested, (4) Oftentimes interested, (3) Sometimes interested, (2) Seldom interested,
or (1) Never interested.

6. Applications.
In practically every research project, a first “look” at the data usually
includes frequency of males and females who participated in the survey,
the number of respondents.
In medical research, one may tabulate the number of patients
displaying specific symptoms; one may tabulate the frequency of different
causes.

7. Frequency Distribution
The easiest method of organizing data is a frequency distribution, which
converts raw data into a meaningful pattern for statistical analysis.
The following are the steps of constructing a frequency distribution:
1. Specify the number of class intervals. A class is a group (category) of interest. No
totally accepted rule tells us how many intervals are to be used.
2. When all intervals are to be the same width, the following rule may be used to find
the required class interval width:
W = (L-S)/N Where:
W = class width
L = the largest data
S = the smallest data
N = number of classes

8. Example: Suppose the ages of a sample of 10 students are:
20.0, 18.1, 18.5, 21.3, 19.4, 25.3, 22.0, 23.1, 23.9, and 23.5
We select N=4 and W=(25.3-18.1)/4 = 1.8 which is rounded-up to 2. The
frequency table is as follows:
Class Interval……..Class Frequency..…….Relative Frequency
18-20……………4……………..40%
21-22……………2……………..20%
23-24……………3……………..30%
25-26…………….1……………..10 %
Note: The sum of all the relative frequency must always be equal to 1.00 or 100%.
In the above example, we see that 40% of all students are younger than 24 years
old, but older than 22 years old.

9. Illustration: Consider the following set of data, which are the scores recorded for
30 participants. We wish to summarize this data by creating a frequency
distribution of the scores.
Data Set- Scores Recorded for 30 Participants
50 45 49 50 43
49 50 49 45 49
47 47 44 51 51
44 47 46 50 44
51 49 43 43 49
45 46 45 51 46

10. To create a frequency distribution from this data
we proceed as follows:
1. Identify the highest and lowest values in the data
set. HS = 51 and LS = 43
2. Create a column with the title of the variable we are using, in
this case score. Enter the highest score at the top, and include
all values within the range from the highest score to the lowest
score.
3. Create a tally column to keep track of the scores as you
enter them into the frequency distribution.
4. Create a frequency column, with the frequency of each
value, as shown in the tally column, recorded.
5. At the bottom of the frequency column record the total
frequency for the distribution proceeded by N=30
6. Enter the name of the frequency distribution at the top
of the table.
Scores Recorded
for 30 Participants
Scores Recorded Tally Frequency
Frequency Distribution
51
50
49
48
47
46
45
44
43
////
////
//////
///
///
////
///
///
4
4
6
0
3
3
4
3
3
N= 30

11. Cumulative Frequency Distribution
A cumulative frequency distribution can be created from a frequency distribution by adding an additional
column called “Cumulative Frequency”
Frequency Distribution Scores Recorded for 30 Participants
Scores Recorded Tally Frequency Cumulative Frequency
Cumulative
51
50
49
48
47
46
45
44
43
////
////
//////
///
///
////
///
///
4
4
6
0
3
3
4
3
3
N= 30
6
3
13
10
16
16
22
26
30

12. Grouped Frequency Distribution
-in some cases it is necessary to group the values of the data to summarize the data properly.
Creating a Grouped Frequency Distribution
1. Find the largest and smallest value.
Data Set – Scores in the Major
Examine (Statistics)
57 39 52 52 43
50 53 42 58 55
58 50 53 50 49
45 49 51 44 54
49 57 55 59 45
50 45 51 54 58
53 49 52 51 41
52 40 44 49 45
43 47 47 43 51
55 55 46 54 41
2. Compute the Range = HS – LS = 20
3. Select the number of classes desired. This is usually 5 to and 20.
4. Find the class width by dividing the range the range by the
number of classes and rounding up.
5. Pick a suitable starting point less than or equal to the
minimum value.
6. To find the upper limit of the first class, subtract one from the
lower limit of the second class.
7. Find the boundaries by subtracting 0.5 units from the lower
limits and adding 0.5units from the upper limits.
8. Tally the data.
9. Find the frequencies.
10. Find the cumulative frequencies. Depending on what you’re trying to accomplish.

13. Grouped Frequency Distribution
-in some cases it is necessary to group the values of the data to summarize the data properly.
Creating a Grouped Frequency Distribution
1. Find the largest and smallest value. 59 and 39.
2. Compute the Range = HS – LS =20
3. Select the number of classes desired. This is usually 5
to and 20.
4. Find the class width by dividing the range the range by the
number of classes and rounding up. =2
5. Pick a suitable starting point less than or equal to the
minimum value.
6. To find the upper limit of the first class, subtract one
from the lower limit of the second class.
7. Find the boundaries by subtracting 0.5 units from the lower
limits and adding 0.5units from the upper limits.
8. Tally the data.
9. Find the frequencies.
Grouped Frequency Distribution for Scores in
the Major Examination (Statistics)
Class
Interval
Tally Interval
Midpoint
Frequency
57
54
51
48
45
42
39
-59
-56
-53
-50
-47
-44
-41
//////
///////
///////////
/////////
///////
//////
////
58
55
52
49
46
43
40
6
7
11
9
7
6
4
N= 50

14. Cumulative Grouped Frequency Distribution for
Scores in the Major Examination (Statistics)
Class
Interval
Tally Interval
Midpoint
Frequency
57
54
51
48
45
42
39
-59
-56
-53
-50
-47
-44
-41
//////
///////
///////////
/////////
///////
//////
////
58
55
52
49
46
43
40
N= 50
Cumulative
Frequency
10. Find the cumulative frequencies. Depending on what you’re trying to accomplish.
50
44
37
26
17
10
4
6
7
11
9
7
6
4

15. B. GRAPHICAL PRESENTATION OF DATA
Several types of statistical/data presentation tools exist, including: (a) charts
displaying frequencies (bar, pie charts), (b) chart displaying trends (run and line
charts), (c) charts displaying distributions (histogram), and (d) charts displaying
associations (scatter diagrams).
Two types of data.
-Attribute Data
are countable data or data that can be put into categories: examples like the
number of people willing to pay, the number of complaints, percentage who want
blue/ percentage who want red.
-Variable Data
are measurement data, based on some continuous scale (length, time, cost).

16. 1. Bar Graph (Histogram)
Bar graphs show quantities represented by horizontal or vertical bars.
FREQUENCY
MARKS

17. 2. Pie Chart or Circle Graph
Pie chats show proportions in relative to a whole, with each wedge representing
a percentage of the total.
43%
19%
14%
14%
5%5%
Adventure Country Family Structures of
9-to-14-Year-Old Youth
live with mother only
live with grand parents
live with one parent and a step parent
live with both parents
Live with father only
other

18. 3. Line Graph (Polygon Method)
Line graphs show sets of data points plotted over a time period and
connected by straight lines.

19. ACTIVITY: (VIDEO PRESENTATION)
Given the following set of data as the actual scores of fifty BSA students in their major examination, prepare a
table showing the following:
1. Class Interval 2. Tally 3. Interval Midpoint 4. Frequency 5. Cumulative Frequency
Data Set – Scores of 50 BSA Students in Major Examination
40 35 58 33 44
63 66 44 25 33
44 40 46 26 55
34 55 78 45 65
41 35 44 27 37
35 57 48 44 48
25 29 56 33 39
44 37 33 55 40
67 28 56 66 50
59 25 37 45 30