maam Lana

▪ Structured numerical decision-making

▪ Quantitative problem solving is a

structured method of identifying a

problem and using numerical data and

statistical tools to find evidence-based

solutions.

▪ It removes guesswork and replaces it

with measurable evidence.

Problem Solving

STEPS IN QUANTITATIVE PROBLEM SOLVING:

1. Identify the problem

2. Define objectives

3. Collect data

4. Analyze data

5. Interpret results

6. Recommend solution
enter done

done

Example 1: Declining Enrollment

Problem: Enrollment dropped by 15%.

Data Collected:

▪ Tuition fee increase: +10%

▪ Competitor school opened nearby

▪ 40% of transferees cite affordability

Decision: Review tuition structure or offer

installment plans.

enter done

done

Example 2: Low Exam Scores

Problem: Average math score = 68%

Data shows:

▪ 70% struggle with algebra

▪ Students study less than 2 hours per

week

Solution:

Add remedial algebra sessions.

enter done

done

Example 3: Business Sales Decline

Problem: Sales dropped ₱50,000 this

quarter.

Data:

▪ Foot traffic decreased by 20%

▪ 60% customers shifted to online

competitors

Solution: Develop online ordering

system.

enter done

done

Example 4: High Employee Turnover

Problem: 30% staff resign yearly.

Survey results:

▪ 50% dissatisfied with salary

▪ 30% dissatisfied with workload

Solution: Adjust salary scale or

redistribute workload.

enter done

done

is the overall strategy and

structure used to conduct research. It

explains how data will be collected,

measured, and analyzed.

a. Research Design

b. Sampling Methods

c. Data Collection Tools

d. Statistical Analysis

Methodology

(Research Design)

Describes characteristics of a population

without manipulating variables.

Example:

Surveying students’ study habits.

Descriptive Research

(Research Design)

Examines relationship between two variables.

Example:

Relationship between study hours and GPA.

Correlational Research

(Research Design)

Manipulates one variable to determine its effect

on another.

Example:

Testing if a new teaching method improves

scores.

Experimental Research

(Research Design)

Similar to experimental but lacks random

assignment.

Example:

Comparing two existing classes using different

teaching styles.

Quasi-Experimental Research

(Sampling Methods)

Every member has equal chance.

Example:

Drawing 100 student IDs randomly.

Simple Random Sampling

(Sampling Methods)

Selecting every kth individual.

Example:

Every 10th student in registry.

Systematic Sampling

(Sampling Methods)

Divide population into groups (strata) and

sample each.

Example:

Select students per grade level

proportionally.

Stratified Sampling

(Sampling Methods)

Select whoever is available.

Example:

Survey students in cafeteria.

Convenience Sampling

Data Collection Tools

▪ Surveys

▪ Interviews

▪ Observation

▪ Tests

▪ Secondary Data

Statistical Analysis

▪ Range, Percentages

▪ Mean, Median, Mode

▪ Standard Deviation

▪ T-test, ANOVA

▪ Correlation (Pearson r)

▪ Linear Regression

A _ _ _ is a simplified numerical or

mathematical representation of a real-

world situation used for prediction and

decision-making.

▪ Simple Formula Models - Uses direct

mathematical formula.

▪ Linear Models - Y = a + bX

where:

Y = dependent variable

a = intercept

b = slope

X = independent variable

▪ Used for prediction & planning

Model

Simple Formula

Model Examples

(Profit = Revenue -Cost)

Case 1:

Revenue = ₱80,000

Cost = ₱50,000

Profit = ₱30,000

Simple Formula

Model Examples

(Profit = Revenue -Cost)

▪ Case 2:

Revenue = ₱60,000

Cost = ₱70,000

Loss = ₱10,000

Simple Formula

Model Examples

(Profit = Revenue -Cost)

▪ Case 3:

Revenue increases by 10%

New revenue = 80,000 × 1.10 = 88,000

Profit = 88,000 − 50,000 = 38,000

Simple Formula

Model Examples

(Break-even Formula)

Break-even = Fixed Cost ÷ (Price −Variable

Cost)

▪ Case 1:

Fixed cost = 20,000

Price = 200

Variable cost = 100

▪ Break-even = 20,000 ÷ 100 = 200 units

Simple Formula

Model Examples

(Break-even Formula)

Break-even = Fixed Cost ÷ (Price −Variable

Cost)

▪ Case 2:

If price increases to 250

Break-even = 20,000 ÷ 150 = 134 units

Simple Formula

Model Examples

(Break-even Formula)

Break-even = Fixed Cost ÷ (Price −Variable

Cost)

▪ Case 3:

If variable cost increases to 120

Break-even = 20,000 ÷ 80 = 250 units

Simple Formula

Model Examples

(Mean Formula)

Mean = Sum of values ÷ Number of values

▪ Case 1:

Scores: 80, 90, 85

Mean = 85

Simple Formula

Model Examples

(Mean Formula)

Mean = Sum of values ÷ Number of values

▪ Case 2:

Scores: 60, 70, 75

Mean = 68.3

Simple Formula

Model Examples

(Mean Formula)

Mean = Sum of values ÷ Number of values

▪ Case 3:

Scores: 95, 88, 92, 85

Mean = 90

▪ Y = a + bX

▪ Used for salary, tuition, sales prediction

Linear Model

Linear Model

Example

(Tuition Increase)

Current tuition = 30,000

Increase = 1,000 yearly

where:

Y = dependent variable

a = intercept (current tuition)

b = slope (yearly increase)

X = independent variable (years)

▪ Model:

Y = a + bX

Y = 30,000 + 1,000X

▪ After 3 years:

Y = 33,000

▪ After 5 years:

Y = 35,000

▪ After 10 years:

Y = 40,000

Linear Model

Example

(Salary Growth)

Starting salary = 20,000

Annual increase = 2,000

where:

Y = dependent variable

a = intercept (Starting salary)

b = slope (annual increase)

X = independent variable (years)

▪ Model:

Y = a + bX

Y = 20,000 + 2,000X

▪ After 2 years:

Y = 24,000

▪ After 4 years:

Y = 28,000

▪ After 6 years:

Y = 32,000

Linear Model

Example

(Salary Growth)

Base sales = 10,000 unitsIncrease per month

= 500

where:

Y = dependent variable

a = intercept (Starting salary)

b = slope (annual increase)

X = independent variable (years)

▪ Model:

Y = a + bX

Y = 10,000 + 500X

▪ After 3 months:

Y = 11,500

▪ After 6 months:

Y = 13,000

▪ After 12 months:

Y = 16,000

Measurement

Scales

▪ Nominal

▪ Ordinal

▪ Interval

▪ Ratio

Scoring Models

▪ Assign weights

▪ Compute weighted score

▪ Select highest total

Managing Data

▪ Data Collection Issues

▪ Published Sources

▪ Internet Sources

▪ Census vs Sample

▪ Market Research

Issues in Data Collection

▪ Bias

▪ Non-response

▪ Measurement Error

▪ Data Entry Error

Published Sources

▪ Philippine Statistics Authority

▪ Department of Education

▪ WHO

▪ World Bank

Survey Methods

▪ Probability Sampling

▪ Non-Probability Sampling

▪ Survey Design

▪ Questionnaire Design

Probability Sampling

Simple Random

Systematic

Stratified

Clusterv

Non-Probability Sampling

Convenience

Purpose
Quote
Snowball

Survey Design Steps

▪ Define Objective

▪ Identify Population

▪ Choose Sampling

▪ Plan Analysis

Questionnaire Design

▪ Clear Questions
Avoid bias

use likert scale

keep concise