Lesson 3

PRESENTATION AND

ORGANIZATION OF DATA

METHODS OF PRESENTING DATA

TABULAR FORM

PARAGRAPH OR TEXTUAL FORM

GRAPHICAL FORM

TABULAR FORM

Data are organize into rows and columns

Statistical table is used to describe the data

Numerical facts are presented in more concise and systematic manner.

PARTS OF STATISTICAL TABLE

TABLE HEAD( TABLE NUMBER AND TABLE TITLE)

BOX HEAD

BODY

FOOTNOTE AND SOURCE (OPTIONAL)

PARAGRAPH /TEXTUAL FORM

Uses sentences or paragraph to describe the data

Combines text and numerical facts

Used if there are only few numerical data and to emphasize on some figures.

GRAPHICAL FORM

Graphs and charts are used to illustrate the data

Graph is a pictorial or geometric representation of data

Presenting more clearly, more creatively in attractive and colorful figures.

PARTS OF STATISTICAL CHARTS

TITLE

COORDINATE AXES

LABELS

LEGEND

SCALE

GRIDLINES

SOURCE(OPTIONAL)

Tabular PRESENTATION

of DATATable 4

Distribution of Students in ABC College According to Year Level

Year Level

Number of Students

First year 300 Second year 250 Third year 285 Fourth year 215

N = 1050 Source: ABC College Registrar

Table number & title

TYPES OF STATISTICAL CHART

• LINE GRAPH• BAR GRAPH• PIE CHART• PICTOGRAPH• STATISTICAL MAP• SCATTER DIAGRAM

BAR GRAPH

A bar graph is used to show relationships between groups.

The two items being compared do not need to affect each other. It's a fast way to show big differences.

Bar Graph is a graph that is useful for comparing the amounts for one set of data.

BAR GRAPH

Base: Class IntervalHeight: Frequency

(c.i) f10 - 14 315 - 19 620 - 24 1225 - 29 730 - 34 435 - 39 3

12

02468

10

10 t

o 14

20 t

o 24

30 t

o 34

There are gaps between bars. This is appropriate to use for discrete variables!

Take Note !!

Bar Chart

Base: Class MarkHeight: Frequency (c.i) f X

10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37

0

2

4

6

8

10

12

12 17 22 27 32 37

There is no gap between bars. This is appropriate to use for continuous variables!

Take Note !!

Histogram

line graph

Line Graph is a graph that is useful for showing how data changes over time.

A line graph is used to show continuing data; how one thing is affected by another.

It's clear to see how things are going by the rises and falls a line graph shows.

LINE GRAPH

PIE CHART

• A PIE CHART is used to show how a part of something relates to the whole.

• This kind of graph is needed to show percentages effectively.

PIE GRAPH

Pie Chart

(c.i) f10 - 14 315 - 19 620 - 24 1225 - 29 730 - 34 435 - 39 3

9%

17%

34%

20%

11%9%

PICTOGRAPH

Pictograph is a graph that uses pictures or symbols to show data.

A pictograph uses an icon to represent a quantity of data values in order to decrease the size of the graph.

PICTOGRAPH

STATISTICAL MAPA statistical map chart displays data by

shading sections of a map, and must include a key.

STATISTICAL MAP

ORGANIZING QUANTITATIVE DATA

• ARRAY – arrangement of data in ascending or descending order

• FREQUENCY DISTRIBUTION- tabular arrangement of data by classes or categories with corresponding frequencies

• STEM AND LEAF PLOT- a representation of a distribution where the individual scores are preserved. Here, the leftmost digit will become the stem and the right digit become the leaf.

Tabular PRESENTATION

of DATA

It is a table which shows the data arranged into different classes and the number of cases which

fall into each class is tallied.

Table 3.0The Ungrouped Frequency Distribution TableFor the Age of 50 Service Crews at Jollimee

Age Frequency Percentage Frequency

18 7 0.14

19 8 0.16

20 6 0.12

21 11 0.22

22 4 0.08

23 5 0.10

24 5 0.10

25 4 0.08

N = 50

Table 3.1The Grouped Frequency Distribution TableFor the Age of 50 Service Crews at Jollimee

Age Frequency Percentage Frequency

18-19 15 0.30

20-21 17 0.34

22-23 9 0.18

24-25 9 0.18

N = 50

Tabular PRESENTATION

of DATA Table 3.2 The Grouped Frequency Distribution for the

Test Scores of 50 Students in Statistics

Class Interval ( c. i )

Tally Frequency ( f )

Class Mark (X)

Class Boundary

3 - 8 9 - 14

15 - 20 21 - 26 27 - 32 33 - 38 39 - 44 45 - 50

I IIII – II IIII – III IIII IIII – IIII - I IIII – III IIII – II IIII

1 7 8 4

11 8 7 4

5.5 11.5 17.5 23.5 29.5 35.5 41.5 47.5

2.5 - 8.5 8.5 – 14.5 14.5 – 20.5 20.5 – 26.5 26.5 – 32.5 32.5 – 38.5 38.5 – 44.5 44.5 – 50.5

N = 50

Tabular PRESENTATION

of DATA

Class Interval(c.i)3 - 89 - 14

15 - 2021 - 2627 - 3233 - 3839 - 4445 - 50

The first column in a frequency distributiontable is the class interval (c.i). The first

column in (c.i) is the lower limit (LL), whilethe second column is the upper limit (UL). There are eight classes in this table, which

starts from 3 - 8 and ends to 45 - 50.

The size of the class interval or the classWidth(c) is 6. It is obtained by getting

the difference between consecutiveupper or lower limits, or by

getting UL - LL + 1unit.Ex. 8 - 3 + 1 = 6

14 - 9 + 1 = 6, ...

TERMINOLOGIES ABOUT FREQUENCY DISTRIBUTION

CLASS INTERVALS

• refers to groups or categories• Example: 8 classes or groups

Class Interval(c.i)3 - 89 - 1415 - 2021 - 2627 - 3233 - 3839 - 4445 - 50

CLASS LIMITS

• Numbers used to name the classes• Example: 9-14 are class limits• Lower class limit is 9• Upper class limit is 14

Table 3.2 The Grouped Frequency Distribution for the

Test Scores of 50 Students in Statistics

Class Interval ( c. i )

Tally Frequency ( f )

Class Mark (X)

Class Boundary

3 - 8 9 - 14

15 - 20 21 - 26 27 - 32 33 - 38 39 - 44 45 - 50

I IIII – II IIII – III IIII IIII – IIII - I IIII – III IIII – II IIII

1 7 8 4

11 8 7 4

5.5 11.5 17.5 23.5 29.5 35.5 41.5 47.5

2.5 - 8.5 8.5 – 14.5 14.5 – 20.5 20.5 – 26.5 26.5 – 32.5 32.5 – 38.5 38.5 – 44.5 44.5 – 50.5

N = 50

CLASS MARK/CLASS MIDPOINT• Xi = (lcli + ucli)/2 where i refers to class number• Grades number class mark

of student• 29-38 3 33.5• 39-48 1 43.5• 49-58 4 53.5• 59-68 10 63.5• 69-78 15 73.5• 79-88 12 83.5• 89-98 5 93.5• TOTAL 50

CLASS BOUNDARIES

• True class limits• Grades class boundaries• 29-38 28.5-38.5• 39-48 38.5-48.5• 49-58 48.5-58.5• 59-68 58.5-68.5• 69-78 68.5-78.5• 79-88 78.5-88.5• 89-98 88.5-98.5• how ? ( 88+89)/2 and (98+99)/2

CLASS WIDTH /CLASS SIZE ( C)

• Difference between 2 consecutive lcl, ucl, lcb, ucb, classmarks

• c= 43.5 –33.5 = 10 using consecutive class marks• c= 38.5 –28.5 = 10 using consecutive ucb• c= 49 –39= 10 using consecutive lcl

number of student

CONSTRUCTION OF FREQUENCY DISTRIBUTION

1. Find the range, R: highest value – lowest value

2. Solve for the number of classes, k

Sturges’ formula k= 1 +3.332 log N

3. Find class size, c

c= R/k

4. Tally

DISTRIBUTIONS DERIVED FROM FREQUENCY DISTRIBUTION

• Relative Frequency Distribution• Cumulative Frequency Distribution

GRAPHICAL REPRESENATATION OF FREQUENCY DISTRIBUTION

• Frequency Histogram- a bar graph to present frequency distribution

• Frequency Polygon- line graph to present frequency distribution

• Ogive- a line graph to present cumulative frequency distribution

FREQUENCY HISTOGRAM• x-axis, classes y-axis, frequency

Base: Class MarkHeight: Frequency (c.i) f X

10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37

0

2

4

6

8

10

12

12 17 22 27 32 37

There is no gap between bars. This is appropriate to use for continuous variables!

Take Note !!

Histogram

FREQUENCY POLYGON

• x-axis, class marks y-axis, frequency

Frequency Polygon

Base: Class MarkHeight: Frequency

(c.i) f X 10 - 14 3 1215 - 19 6 1720 - 24 12 2225 - 29 7 2730 - 34 4 3235 - 39 3 37

0

2

4

6

8

10

12

14

7 12 17 22 27 32 37 42

This is appropriateto use for

continuous variables!

Take Note !!Additional “X” areadded on both ends in orderto close the polygon.

OGIVE

• LINE GRAPH TO PRESENT THE CUMULATIVE FREQUENCY DISTRIBUTION

• x-axis, class boundaries• y-axis, cumulative frequency

< Ogive Base: Upper Class Boundary Height: < cf

c.b. <cf - 9.5 0 9.5-14.5 3 14.5-19.5 9 19.5-24.5 21 24.5-29.5 28 29.5-34.5 32 34.5-39.5 35

0

5

10

15

20

25

30

35

40

9.5 14.5 19.5 24.5 29.5 34.5 39.5

< Ogive

There is additionalUpper c.b. “9.5” with<cf equal to 0.

Take Note !!

> Ogive Base: Lower Class Boundary Height: > cf

c.b. >cf 9.5-14.5 3514.5-19.5 3219.5-24.5 2624.5-29.5 1429.5-34.5 734.5-39.5 339.5- 0

>cf & Lower c.b. 0

5

10

15

20

25

30

35

40

9.5 14.5 19.5 24.5 29.5 34.5 39.5

> Ogive

There is additionalLower c.b. “39.5” with>cf equal to 0.

Take Note !!

Ogives Base: Class IntervalHeight: Cumulative Frequency

0

5

10

15

20

25

30

35

40

9.5 14.5 19.5 24.5 29.5 34.5 39.5

<cf & Upper c.b.>cf & Lower c.b.

< Ogive

> Ogive

c.b. <cf >cf 9.5-14.5 3 3514.5-19.5 9 3219.5-24.5 21 2624.5-29.5 28 1429.5-34.5 32 734.5-39.5 35 3

The Contingency TableThis is a table which shows the data

enumerated by cell.

Table 3.5The Contingency Table for the Opinion of Viewers

on the New TV Program

34097127116Total

138405543Do not like the program

51121623Indifferent

151455650Like the program

TotalChildrenWomenMenChoice/Sample