Notes, summaries, assignments, exams, and problems for Mathematics

Fundamentals of Statistical Analysis

Frequency Distribution

Ungrouped Data

Ungrouped data are lists of observed values when the pooled data represent a mass of observed data.

Pooled Data

When data are grouped in a frequency distribution.

• Collect data and make a tally sheet

Determination of Range

The range is the difference between the highest observed value and the lowest value observed.

Determining the Range of Classes

The range of classes is the enactment between the midpoint of classes.

Determine the Midpoints of the Class

The midpoint of the class must include the minimum data value in that class.

Determine the Class Boundaries

The class limits are the extreme values or limits of a class and are called the upper limit and lower limit.

Identify the Frequency

Grounded Theory: Strategies and Methods

Grounded theory has two main strategies:

Theoretical Sampling

Involves adding to the sample of subjects or situations encountered, additional comments, or further interviews. It seeks to find different cases.

Constant Comparative Method

It is a method to analyze the data at different times in which the researcher interacts with:

1. Classified portions of data:
   • Words
   • Phrases
   • Paragraphs

Categories arise, either intuited or implicit (they are marked, but without a name).

Constant Comparative Method

As the process of selecting pieces of data advances, categories appear with more explicit rules.

The task is to identify:

1. Emerging categories = Issues
   • Categories = Properties
2. Central category = Recurring Themes

Links between categories... Continue reading "Grounded Theory: Strategies, Methods, and Analysis" »

Substance Concentration Data Grouping

The content of a substance in a liquid is given with an accuracy of 5 milligrams per liter. As such, the data can take values from this sequence:

• 120
• 125
• 130
• 135
• 140
• 145

Grouping Amplitude and Frequency Table Construction

The problem states a data set ranging between 110 and 245. However, the provided calculation for the number of steps, (247.7 - 107.5) / 25 = 5.6, implies a wider range. This calculation indicates that 6 steps (intervals) of 25 units each are needed. Since 6 intervals of 25 units cover 150 units, the apparent limits can be started with a round number to accommodate the required range.

**Purchase Operations**

Shopping is any transaction by which a person receives the domain of property for valuable consideration. The purchase consists of two stages or operations:

**Request for Purchase or Requisition of Goods**

This is a formal request made by a department or warehouse operations, being directed to the purchasing department.

**Order Form**

The purchasing department receives the application and analyzes the real need, according to the financial situation and market conditions, as the article refers.

**Reception Guide**

This is a document issued by the warehouse when it acquires the goods from suppliers. Prior to the receipt, the warehouse manager must take care to verify if the merchandise received matches the packing list issued... Continue reading "Purchase and Sales Operations: Essential Documents" »

Key Warehouse Functions

Departure

• Monitor the consumption of items by various departments.
• Suitably distribute articles.

Entry

• Reject material that does not meet the requirements of the order.
• Monitor and handle the exchange of expired material.

Storage

• Protect and oversee all the products stored.
• Register and control the movements of stock.
• Avoid losses in the stored materials.
• Ensure items are consumed before the expiry date.
• Design documents necessary for good control of the warehouse.
• Request resupply when stocks are minimal.

When to Start Product Replacement

Replacement of a product should start before falling below the minimum stock.

High Maximum Stock: Advantages and Disadvantages

Maximum stock refers to the maximum amount of a particular item above... Continue reading "Warehouse Functions and Inventory Management in Healthcare" »

Management Control Instruments

Planning

Establishes lines of action and responsibility within a company's organization to achieve goals. This is executed through programs and embodied in the budget applicable to each program.

Budget

Determines objectives more precisely, specifying amounts and responsible parties. The budget, when applied to the immediate future, is known as operational planning. It is typically performed for a period of days or weeks, using fully quantitative variables and involving the direct participation of each department.

Causes of Deviations

Deviation Definition

A deviation is the difference that arises when comparing expected (planned or budgeted) data with actual results.

Sources of Deviations

• Errors in environmental estimates:

Case Study 1: Sales Team Head Settlement

Employee Details & Salary Structure

Settlement Calculation Steps

Unpaid Salary

• Period: November 1 - November 3 (3 days)

Monthly Salary = 1,090 + 320 + 90 = 1,500 Euros/month

Unpaid Salary for 3 days = (1,500 / 30) * 3 = 150 Euros

Pro-rata

VAT Fees Eligible for Deduction

The following fees can be deducted:

• Submission-entry of goods from another taxable person
• Imports of goods
• Intra-Community acquisitions
• Fees relating to cases of reverse charge

Partial Deduction or Pro Rata

This applies when a company performs two types of activities: operations with deduction and operations without deduction.

The consequence is that only a portion or percentage of the taxes charged can be deducted.

What percentage? To determine the coefficient, calculate the following:

(Sum of output-delivery deduction in the year) / (Sum of all delivery-end of the year)

To calculate the deduction, multiply the percentage by the taxes charged.

Dynamics During the Exercise: Provisionally apply the percentage from the previous... Continue reading "VAT Deduction Rules: Fees, Partial Deduction, and Investment" »

Frequency Distribution

1) Loose Data: Data collected that has not been organized numerically. For example, heights of males and females obtained from a survey, arranged alphabetically.

2) Ordination: An arrangement of numerical data in ascending or descending order. The difference between the largest and smallest number is called the data range.

Example:

Data Management Data Range
2.1 1 A: 10 to 1
7.6 2 R: 9
4.9 4
8.10 6 R: range of the data.
7
8
9
10

3) Frequency Distribution: When dealing with large amounts of loose data, it's useful to distribute them into classes or categories and determine the number of individuals belonging to each category, often called a class.

A tabular distribution of data by type or category with its corresponding... Continue reading "Understanding Frequency Distributions: Data Organization" »

Types of Research

Descriptive and Explanatory Research

Descriptive Research: Aims to show a situation or phenomenon.

Explanatory Research: Seeks to uncover the truth of a hypothesis.

Transverse and Longitudinal Research

Transverse Research: Involves studying different variables at a specific point in time.

Longitudinal Research: Involves studying variables over an extended period.

Retrospective and Prospective Research

Retrospective Research: Observation units are classified based on the presence or absence of an effect, and the frequency of causal factors is recorded.

Prospective Research: Individuals are selected based on the presence or absence of exposures (inputs), and the frequency of the effect is recorded.

Case-Control Studies

• Combines advantages