Mathematics 101: Tabular and Graphical Presentation of Data Olive - - PowerPoint PPT Presentation

Mathematics 101:

Tabular and Graphical Presentation of Data

Olive R. Cawiding Department of Mathematics and Computer Science University of the Philippines Baguio

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Overview

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data

Data can be presented by incorporating it to a paragraph of text. Examples:

“The Philippines’ annual inflation rate rose to 5.7 percent in July of 2018 from 5.2 percent in the previous month, above market estimates

• f 5.5 percent. It is the highest reading since March 2009. On a

monthly basis, consumer prices went up 0.5 percent, after a 0.6 percent rise in June.” -Trading Economics “Employment rate in Philippines decreased to 94.50 percent in the second quarter of 2018 from 94.70 percent in the first quarter of 2018. Employment Rate in Philippines averaged 91.22 percent from 1991 until 2018, reaching an all time high of 95.30 percent in the fourth quarter of 2016 and a record low of 85.60 percent in the second quarter of 1991.”-Trading Economics

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data

Important Questions.

• 1. When is it appropriate to use textual presentation of data?
• 2. What are possible disadvantages of textual presentation of

data?

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Overview

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Tabular Presentation of Data

Data can also be presented by means of tables. This is a systematic organization of data using columns and rows. What are its advantages over a textual presentation of data?

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Tabular Presentation of Data

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Parts of a Formal Statistical Table

• 1. Heading - consists of a table number, title, and headnote.
• The title is a brief statement of the nature, classification and

time reference of the information presented and the area to which the statistics refer.

• The headnote is a statement enclosed in brackets between the

table title and the top rule of the table that provides additional title information.

• 2. Box Head - the portion of the table that contains the

column heads and spanner heads

• The column heads describe the data in each column, together

with the necessary and qualifying spanner heads.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Parts of a Formal Statistical Table

• 3. Stub - the portion of the table usually comprising the first

column on the left, in which the stubhead and row captions, together with the needed classifying and qualifying centerhead and subheads are located.

• The stubhead describes the stub listing as a whole in terms of

the classification presented.

• The row caption is a descriptive title of the data on the given

line.

• 4. Field - main part of the table; contains the substance or the

figures of one’s data.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Parts of a Formal Statistical Table

• 5. Source Data - an exact citation of the source of data

presented in the table (should always be placed when figures are not original)

• 6. Footnote - any statement or note inserted at the bottom of

the table What should be taken note of when creating a statistical table?

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Overview

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of Data

A graph or chart is a device for showing numerical values or relationships in pictorial form.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of Data

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of Data

Qualities of a Good Graph

• 1. Accuracy
• 2. Clarity
• 3. Simplicity
• 4. Appearance

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Line Chart

A line chart is a graphical presentation of data especially useful for showing trends over a period of time.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Bar Chart

A bar chart consists of a series of rectangular bars where the length of the bar represents the quantity of frequency for each category if the bars are arranged horizontally. If the bars are arranged vertically, the height of the bar represents the quantity.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Bar Chart

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Pie Chart

A pie chart a circular graph that is useful in showing how a total quantity is distributed among a group of categories. The “pieces of pie” represent the proportions of the total that fall into each category.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Pie Chart

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Common Types of Graphs: Pie Chart

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Pictorial Unit Chart

A pictorial unit chart is a chart in which each symbol represents a definite and uniform value.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Overview

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

Definition.

The raw data is the set of data in its original form. Example: The final grades of Math 101 students are as follows.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

Definition.

An array is an arrangement of observations according to their magnitude, either in increasing or decreasing order. Example: The final grades (in an array) of Math 101 students are as follows. 50 57 63 69 72 74 77 80 82 84 87 50 59 65 69 72 75 77 80 82 84 87 50 59 66 69 72 75 77 80 82 85 88 50 60 66 69 72 75 77 81 83 85 89 50 60 68 70 73 75 78 81 83 86 89 50 60 68 71 73 75 79 81 84 86 91 51 62 68 71 73 76 79 81 84 87 92 52 62 68 71 73 76 79 82 84 87 94 53 62 68 71 74 76 79 82 84 87 94 53 62 69 72 74 76 79 82 84 87 96

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

A frequency distribution is the organization of raw data in table form, using classes and frequencies. The frequency distribution table shows the number of items falling into each group.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

Class Freq. LCB UCB CM RF RFP < CF > CF 50 − 54 10 49.5 54.5 52 0.09 9 10 110 55 − 59 3 54.5 59.5 57 0.03 3 13 100 60 − 64 8 59.5 64.5 62 0.07 7 21 97 65 − 69 13 64.5 69.5 67 0.12 12 34 89 70 − 74 17 69.5 74.5 72 0.15 15 51 76 75 − 79 19 74.5 79.5 77 0.17 17 70 59 80 − 84 22 79.5 84.5 82 0.20 20 92 40 85 − 89 13 84.5 89.5 87 0.12 12 105 18 90 − 94 4 89.5 94.5 92 0.04 4 109 5 95 − 99 1 94.5 99.5 97 0.01 1 110 1

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

Definition of terms.

• 1. Class frequency - the number of observations falling in the

class.

• 2. Class interval - the numbers defining the class
• 3. Class limits - the end numbers of the class
• 4. Class boundaries - the true class limits
• The lower class boundary (LCB) is usually defined as halfway

between the lower class limit of the class and the upper class limit of the preceding class.

• The upper class boundary (UCB) is usually defined as halfway

between the upper class limit of the class and the lower class limit of the next class

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

The Frequency Distribution Table

Definition of terms.

• 4. Class size - the difference between the upper class

boundaries of the class and the preceding class; can also be computed as the difference between the lower class boundaries of the current class and the next class; can also be computed by using the respective class limits instead of the class boundaries

• 5. Class mark (CM) - midpoint of a class interval
• 6. Open-end class - class that has no lower limit or upper

limit

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Steps in Constructing a Frequency Distribution Table

• 1. Determine the number of classes. Two of the most common

ways of determining this are:

• Sturges’ Formula. The approximate number K of classes is

given by K = 1 + 3.322 log n where n is the number of observations.

• K =

√ number of observations

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Steps in Constructing a Frequency Distribution Table

• 2. Determine the approximate class size. The following steps can

be used to determine the class size.

(a) Solve for the range, R = max − min (b) Compute C′ = R ÷ K. (c) Round off C′ to C which has the same number of decimal places as the original data set. Use C as the class size.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Steps in Constructing a Frequency Distribution Table

• 3. Determine the lower class limit. The first class must include

the smallest value in the data set and must agree with the number of decimal places in the data set.

• 4. Determine all class limits, by adding the class size C, to the

limit of the previous class.

• 5. Tally the frequencies for each class. Sum the frequencies and

check against the total number of observations.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Variations of the Frequency Distribution

• 1. Relative Frequency (RF) and Relative Frequency

Percentage RF = class frequency ÷ no. of observations RFP = RF ∗ 100

• 2. Cumulative Frequency Distribution (CFD) shows the

accumulated frequencies of successive classes, beginning at either end of the distribution.

> CFD shows the number of observations greater than the LCB. < CFD shows the number of observations less than the UCB.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of the Frequency Distribution Table

The frequency histogram is a bar graph that displays the classes on the horizontal axis and the frequencies of the classes on the vertical axis; the vertical lines of the bars are erected at the class boundaries and the height of the bars correspond to the class frequency.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of the Frequency Distribution Table

The frequency polygon is a line chart that is constructed by plotting the frequencies at the class marks and connecting the plotted points by means of straight lines; the polygon is closed by considering an additional class at each end and the ends of the lines are brought down to the horizontal axis at the midpoints of the additional classes.

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of the Frequency Distribution Table

Ogives are graphs of the cumulative frequency distribution (a) < ogive - the < CF is plotted against the UCB (b) > ogive - the > CF is plotted against the LCB

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of the Frequency Distribution Table: <Ogive

Textual Presentation of Data Tabular Presentation of Data Graphical Presentation of Data The Frequency Distribution Table

Graphical Presentation of the Frequency Distribution Table: >Ogive