MODULE 4
MATHEMATICS AS A TOOL FOR BUSINESS AND FINANCE

LESSON NO.	1
LESSON TITLE	Data Presentation Tools
DURATION/ HOURS	3 hours
Specific Learning Outcomes:	During the learning engagements, the students should be able to: 1. Construct and interpret frequency distribution tables 2. Construct and interpret different graphs
TEACHING LEARNING ACTIVITIES
PROCESSING Data Presentation This refers to the organization of data into tables, graphs or charts, so that logical and statistical conclusions can be derived from the collected measurements. Data can be presented in 3 forms: 1. Textual Form – gathered data are presented in paragraph form – data are written and read – combination of texts and figures Example: Of the 150 sample interviewed, the following complaints were noted: 27 for lack of books in the library, 25 for a dirty playground, 20 for lack of laboratory equipment, 17 for a not well maintained university buildings. 2. Tabular Form – a systematic organization of data in columns and rows. – using statistical table Parts of Statistical Table: (1) Table Heading – consist of table number and title; (2) Stubs – classifications/categories which are found at the left side of the body of the table; (3) Box head – main part of the table; (4) Footnotes – any statement or note inserted; (5) Source note – source of the statistics

3. Graphical Form Kinds of Graphs  Bar Graph – used to show relationship/comparison between groups  Pie or Circle Graph – shows percentages effectively  Line Graph – most useful in displaying data that changes continuously overtime  Pictograph – or pictogram. It uses identical or figures of objects called isotopes in making comparisons. Each picture represents a definite quantity A histogram is a graphical display of data using bars of different heights. In a histogram, each bar groups numbers into ranges. Taller bars show that more data falls in that range. A histogram displays the shape and spread of continuous sample data.

Bar Graph Line Graph
Pie/Circle Graph Pictograph
Histogram

STATISTICAL PRESENTATIONS: FREQUENCY DISTRIBUTION TABLE A frequency distribution table is one way you can organize data so that it makes more sense. In statistics, a frequency distribution is a list, table or graph that displays the frequency of various outcomes in a sample. Each entry in the table contains the frequency or count of the occurrences of values within a particular group or interval. For example, let’s say you have a list of IQ scores for a gifted classroom in a particular elementary school. The IQ scores are: 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154. That list doesn’t tell you much about anything. You could draw a frequency distribution table, which will give a better picture of your data than a simple list. Part 1: Choosing Classes Step 1: Figure out how many classes (categories) you need. There are no hard rules about how many classes to pick, but there are a couple of general guidelines: Pick between 5 and 20 classes. For the list of IQs above, we picked 5 classes. Make sure you have a few items in each category. For example, if you have 20 items, choose 5 classes (4 items per category), not 20 classes (which would give you only 1 item per category). Part 2: Sorting the Data Step 2: Subtract the minimum data value from the maximum data value. For example, our IQ list above had a minimum value of 118 and a maximum value of 154, so: 154 – 118 = 36 Step 3: Divide your answer in Step 2 by the number of classes you chose in Step 1. 36 / 5 = 7.2 Step 4: Round the number from Step 3 up to a whole number to get the class width. Rounded up, 7.2 becomes 8. Step 5: Write down your lowest value for your first minimum data value: The lowest value is 118 Step 6: Add the class width from Step 4 to Step 5 to get the next lower class limit: 118 + 8 = 126 Step 7: Repeat Step 6 for the other minimum data values (in other words, keep on adding your class width to your minimum data values) until you have created the number of classes you chose in Step 1. We chose 5 classes, so our 5 minimum data values are: 118 126 (118 + 8) 134 (126 + 8) 142 (134 + 8) 150 (142 + 8) Step 8: Write down the upper class limits. These are the highest values that can be in the category, so in most cases you can subtract 1 from the class width and add that to the minimum data value. For example: 118 + (8 – 1) = 125 118 – 125 126 – 133 134 – 141 142 – 149 150 – 157

3. Finishing the Table Up Step 9: Add a second column for the number of items in each class, and label the columns with appropriate headings: Step 10: Count the number of items in each class, and put the total in the second column. The list of IQ scores are: 118, 123, 124, 125, 127, 128, 129, 130, 130, 133, 136, 138, 141, 142, 149, 150, 154. There are some statistical frequency tables that include cumulative frequency (cf), relative frequency (rf), and cumulative relative frequency (cf).  The cumulative frequency is calculated by adding each frequency from a frequency distribution table to the sum of its predecessors. The last value will always be equal to the total for all observations, since all frequencies will already have been added to the previous total. See the illustration below  To find the relative frequency, divide the frequency by the total number of data values. See the colored illustration.  To find the cumulative relative frequency, add all of the previous relative frequencies to the relative frequency for the current row. See the colored illustration. Let’s take the finished frequency distribution table example previously… IQ (X)Frequency (f)Cumulative Frequency (cf)Relative Frequency (rf)Cumulative Relative Frequency (crf)150-157 2 17 2÷17=0.12 1.01 or 1.00142-149 2 15 0.12 0.89134-141 3 13 0.18 0.77126-133 6 10 0.35 0.59118-125 4 4 0.24 0.24∑f= 17

There are some statistical frequency tables that include Class Boundary and Class Mark  The lower class boundary is found by subtracting 0.5 units from the lower class limit and the upper class boundary is found by adding 0.5 units to the upper class limit. The difference between the upper and lower boundaries of any class. See the colored illustration.  The “midpoint” (or “class mark”) of each class can be calculated as: Midpoint = Lower class limit + Upper class limit 2 The “relative frequency” of each class is the proportion of the data that falls in that class. Let’s take the finished frequency distribution table example previously… IQ (X)Frequency (f)Class Boundary Class Mark150-157 2 149.5-157.5 153.5142-149 2 141.5-149.5 145.5134-141 3 133.5-141.5 137.5126-133 6 125.5-133.5 129.5118-125 4 117.5-125.5 121.5∑f= 17Activity 1: Present your data Construct a (1) complete frequency distribution table and (2) a most appropriate graph suitable to the data given with (3) Comprehensive Textual presentation.The following are the test scores of the class (suppose: the 50-item midterm test scores of 30 college students in the MMW subject) Note: Ensure that the table and graph have COMPLETE details, parts, and labels. 45 43 40 47 45 35 30 50 48 42 50 38 48 35 30 43 50 29 46 50 43 44 39 38 46 50 43 44 42 49 (1) Frequency Distribution Table Class Interval (X)frequency (f)Class BoundaryClass MarkCumulative Frequency (cf)Relative Frequency (rf)Cumulative Relative Frequency (crf)∑f=(2) GRAPHICAL PRESENTATION (3) Discussions and Interpretations (TEXTUAL PRESENTATION)

SYNTHESIS ACTIVITY: 1. How important are data presentation tools? What must be considered when constructing a table and a graph? 2. When doing textual presentation of data, what necessary details should be considered?

ASSESSMENTS

I. Multiple Choice. Encircle your best choice. 1. Alex needs to convey some precise financial information to his company’s Board of Directors in a quarterly report. How should he present this information? a. Using a line chart b. Using text on PowerPoint slide c. Using a Table d. Using a pie chart 2. A data table has a. an X and Y axis b. rows and columns c. bars d. all of the above 3. Data tables are often easier to understand than long list of raw data. a. True b. False 4-5. Refer from the figure below. 4. Which month had the highest average temperature? a. June b. July c. August d. September

5. Which month had the lowest average temperature? a. January b. February c. March d. April I. Drawing Conclusions. Give as many findings as you can and draw as many conclusions from your findings. Refer from the given table below. Discussions, Interpretations, and Conclusion:
RESOURCES:	1. http://academic.sun.ac.za/emergencymedicine/TRRM/module5/BS1-3.htm 2. https://www.slideshare.net/WinonaEselBernardo/presentation-of-data- 10958540 3. https://study.com/academy/practice/quiz-worksheet-using-textual-and-visual graphics-to-present-data.html 4. https://www.educba.com/what-is-business-mathematics/ 5. https://www.slideshare.net/rubyocenar/presentation-of-data-37973327