mathematics 101: tabular and graphical presentation of data...aug 03, 2018 · graphical...

Mathematics 101:Tabular and Graphical Presentation of Data

Olive R. CawidingDepartment 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



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 of2018 from 5.2 percent in the previous month, above market estimatesof 5.5 percent. It is the highest reading since March 2009. On amonthly basis, consumer prices went up 0.5 percent, after a 0.6percent rise in June.” -Trading Economics

“Employment rate in Philippines decreased to 94.50 percent in thesecond quarter of 2018 from 94.70 percent in the first quarter of 2018.Employment Rate in Philippines averaged 91.22 percent from 1991until 2018, reaching an all time high of 95.30 percent in the fourthquarter of 2016 and a record low of 85.60 percent in the secondquarter of 1991.”-Trading Economics



Important Questions.

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

data?


Overview







Data can also be presented by means of tables. This is asystematic organization of data using columns and rows.

What are its advantages over a textual presentation of data?


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 towhich the statistics refer.

• The headnote is a statement enclosed in brackets between thetable title and the top rule of the table that provides additionaltitle information.

2. Box Head - the portion of the table that contains thecolumn heads and spanner heads• The column heads describe the data in each column, together

with the necessary and qualifying spanner heads.



3. Stub - the portion of the table usually comprising the firstcolumn on the left, in which the stubhead and rowcaptions, together with the needed classifying andqualifying 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.



5. Source Data - an exact citation of the source of datapresented in the table (should always be placed whenfigures are not original)

6. Footnote - any statement or note inserted at the bottom ofthe table

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


Overview







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



Qualities of a Good Graph1. Accuracy2. Clarity3. Simplicity4. Appearance


Common Types of Graphs: Line Chart

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


Common Types of Graphs: Bar ChartA bar chart consists of a series of rectangular bars where thelength of the bar represents the quantity of frequency for eachcategory if the bars are arranged horizontally. If the bars arearranged vertically, the height of the bar represents the quantity.


Common Types of Graphs: Bar Chart


Common Types of Graphs: Pie Chart

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


Common Types of Graphs: Pie Chart


Pictorial Unit ChartA pictorial unit chart is a chart in which each symbolrepresents a definite and uniform value.


Overview







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


The Frequency Distribution TableDefinition.An array is an arrangement of observations according to theirmagnitude, either in increasing or decreasing order.Example: The final grades (in an array) of Math 101 studentsare as follows.

50 57 63 69 72 74 77 80 82 84 8750 59 65 69 72 75 77 80 82 84 8750 59 66 69 72 75 77 80 82 85 8850 60 66 69 72 75 77 81 83 85 8950 60 68 70 73 75 78 81 83 86 8950 60 68 71 73 75 79 81 84 86 9151 62 68 71 73 76 79 81 84 87 9252 62 68 71 73 76 79 82 84 87 9453 62 68 71 74 76 79 82 84 87 9453 62 69 72 74 76 79 82 84 87 96



A frequency distribution is the organization of raw data in tableform, using classes and frequencies. The frequencydistribution table shows the number of items falling into eachgroup.



Class Freq. LCB UCB CM RF RFP < CF > CF50− 54 10 49.5 54.5 52 0.09 9 10 11055− 59 3 54.5 59.5 57 0.03 3 13 10060− 64 8 59.5 64.5 62 0.07 7 21 9765− 69 13 64.5 69.5 67 0.12 12 34 8970− 74 17 69.5 74.5 72 0.15 15 51 7675− 79 19 74.5 79.5 77 0.17 17 70 5980− 84 22 79.5 84.5 82 0.20 20 92 4085− 89 13 84.5 89.5 87 0.12 12 105 1890− 94 4 89.5 94.5 92 0.04 4 109 595− 99 1 94.5 99.5 97 0.01 1 110 1



Definition of terms.

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

2. Class interval - the numbers defining the class3. Class limits - the end numbers of the class4. 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 classlimit of the preceding class.

• The upper class boundary (UCB) is usually defined as halfwaybetween the upper class limit of the class and the lower classlimit of the next class



Definition of terms.

4. Class size - the difference between the upper classboundaries of the class and the preceding class; can also becomputed as the difference between the lower classboundaries of the current class and the next class; can alsobe computed by using the respective class limits instead ofthe class boundaries

5. Class mark (CM) - midpoint of a class interval6. Open-end class - class that has no lower limit or upper

limit


Steps in Constructing a Frequency Distribution Table

1. Determine the number of classes. Two of the most commonways of determining this are:• Sturges’ Formula. The approximate number K of classes is

given byK = 1 + 3.322 log n

where n is the number of observations.

• K =√

number of observations



2. Determine the approximate class size. The following steps canbe 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.



3. Determine the lower class limit. The first class must includethe smallest value in the data set and must agree with thenumber of decimal places in the data set.

4. Determine all class limits, by adding the class size C, to thelimit of the previous class.

5. Tally the frequencies for each class. Sum the frequencies andcheck against the total number of observations.


Variations of the Frequency Distribution

1. Relative Frequency (RF) and Relative FrequencyPercentage

RF = class frequency÷ no. of observationsRFP = RF ∗ 100

2. Cumulative Frequency Distribution (CFD) shows theaccumulated frequencies of successive classes, beginningat either end of the distribution.

> CFD shows the number of observations greater than theLCB.

< CFD shows the number of observations less than theUCB.


Graphical Presentation of the FrequencyDistribution Table

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



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



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


Graphical Presentation of the FrequencyDistribution Table: <Ogive


Graphical Presentation of the FrequencyDistribution Table: >Ogive

mathematics 101: tabular and graphical presentation of data...aug 03, 2018 · graphical...

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