Data Presentation in MATH154-1

Course Outcome 1: Data Presentation

• Course: MATH154-1 Quantitative Methods
• University: Mapua University
• Objective: Students will learn various methods of data presentation, describe and interpret data, and practice applying different methods.

Types of Data Presentation

• Textual Form: Presenting data using sentences and paragraphs to describe the data.
• Tabular Form: Presenting data using tables arranged in rows and columns to organize different parameters.
• Graphical Form/Pictorial Form: Pictorial representation of data. This includes visual representations of the data.

Data Presentation Types

• Ungrouped Data: Individual data points are treated separately.
• Grouped Data: Data points are grouped according to categories.

Frequency Distribution Table

• Analyze numerous data: Group the data into classes with equal intervals.
• Determine frequency: Count the number of observations in each class.
• Less work: This method reduces the work of treating each data point individually.

Class Limits

• Smallest and largest values: Define the class interval that includes the lowest and highest values.
• Significant figures: Use the same number of significant figures as the given data.

Class Boundaries

• True class limits: Precise expression of the class interval.
• Extra significant digit: Usually one significant digit greater than the class limit.
• Midpoint calculation: Calculated at the midpoint of the lower class limit and the upper class limit.

Frequency

• Number of Observations The frequency represents the number of observations within a specific class.
• Counting & Tallying Counting and tallying are the methods that help in determining the frequency.

Class Width (Class Size)

• Numerical Difference: The difference between the upper and lower class boundaries.

Class Mark (Class Midpoint)

• Middle Element: Represents the middle element of a class.
• Symbolized by 'x': Usually symbolized by 'x'.

Cumulative Frequency Distribution

• Derived from frequency distribution: Cumulative frequency distributions are derived from frequency distribution tables.

• Adding class frequencies: Adding the class frequencies to obtain cumulative frequencies.

• Partial sums: Cumulative frequency distributions can also be calculated through partial sums.

• Less than cumulative frequency: (<cf) representing frequencies less than/or equal to the upper class boundary.

• Greater than cumulative frequency: (>cf) representing frequencies greater than/or equal to the lower class boundary.

Relative Frequency

• Percentage frequency: The percentage frequency of a class relative to the total population.
• Pie charts: Used for presenting pie charts.

Relative Frequency Distribution

• Percentage proportion: The proportion in percentages of each class's frequency to the total frequency.
• Obtain frequency: Obtained by dividing the class frequency by the total frequency and then multiplying by 100.

Frequency Distribution Table

• Detailed Table: This table is designed to present data in a structured format with columns like class intervals, frequencies, lower class boundaries (LCB), upper class boundaries (UCB), less than cumulative frequency, greater than cumulative frequency and percentage frequency.

Steps in Constructing a Frequency Distribution Table (FDT)

1. Identify the highest and lowest values.
2. Calculate the range (R=H-L).
3. Determine the number of classes (k). [k = 1 + 3.322log⁡n].
4. Calculate the class size (C=R/k).
5. Set the lower limit of the first class interval.
6. Determine class frequencies by counting data points.

Graphical Forms of Frequency Distribution

• Frequency Polygon: Line graph using class midpoints as x-coordinates and frequencies as y-coordinates.
• Histogram: Bar graph using class limits as the bases of rectangles. The height of each bar corresponds to its class frequency. Using exact lower class limits.
• Ogive: Line graph representing cumulative frequencies. Distinguishes cf ogives based on whether they're greater than or less than the boundary value.

Stem-and-Leaf Diagram

• Tabular form: A way to present data.

Additional Information

• Example Data Sets: Sample data for 50 students in a math quiz, and thicknesses of metal parts.

This quiz covers various methods of data presentation, including textual, tabular, and graphical forms. Students will learn to describe, interpret, and apply these methods effectively, focusing on both ungrouped and grouped data, as well as frequency distribution tables.