Notes, summaries, assignments, exams, and exercises for Mathematics for Baccalaureate

Chapter 3: Key Concepts

Missing Variable

x = given Median * 2 - ((1 of 2) median numbers if even): ascending order

Unreadable Score

(U * N of unreadable) - (U * N of readable)

Degrees of Freedom

1 # of freedom is lost

Chebyshev's Theorem

K = Deviation

Calculate time % within K Dev of mean - (1 - 1/k^2) * 100 = %

Finding Values

Find x K devs from mean - (mean - K * given standard dev) = XLow...(mean + k * given standard dev) = XHigh

Finding % Within Times Xlow-Xhigh

K = (XHigh - Mean) / Given Standard dev....then do Chebyshev's - (1 - 1/k^2) * 100 = %

Z-Score Simplified

(Mean - Given Mean) / Given Standard Dev = ZScore

Finding Minimum Score Accepted

(Min devs) * (Given Devs) + (Mean) = Min Score

Weighted Mean

Chart Xi / Wi /XiWi

Use Empirical Rule if distribution

Qualitative and Quantitative Variables

Qualitative: variables that are not numerical. They represent categories or groups that the data can fall into. Nominal: the categories do not have a natural order or ranking. The key characteristic of nominal variables is that the different categories are mutually exclusive and there is no inherent order to the categories. Ordinal: the categories have a logical or natural order. However, the distances between the categories are not necessarily meaningful.

Quantitative: variables that represent quantities and can be measured numerically. Discrete: a type of quantitative variable that can take on a countable number of distinct values. These are typically values that you can list or count. They often represent...

Checks: A Comprehensive Overview

What is a Check?

A check is a document instructing a bank (the drawee) to pay a specific amount of money to the check holder (the payee) from the account of the person who wrote the check (the drawer).

Parties Involved

• Drawer: The person who writes and signs the check, authorizing the payment.
• Drawee: The bank or financial institution where the drawer has an account.
• Payee/Holder: The person or entity to whom the check is made payable.
• Guarantor: A person who guarantees payment if the drawer's account has insufficient funds.
• Endorser: The payee who signs the back of the check to transfer ownership.
• Endorsee: The person to whom the check is endorsed.

Types of Checks

Forms of Writing

• Bearer: Payable to the person holding

Parameter vs. Statistic

Parameter: Population (μ, σ)

Statistic: Sample (x̄, s)

Rules of Probability

1. 0 ≤ P(x) ≤ 1
2. Σ P(x) = 1
3. P(not x) = 1 - P(x)

Central Limit Theorem

As n (sample size) gets bigger, the sample distance will become approximately normal (shape).

Law of Large Numbers

As n gets bigger, the sample mean (x̄) will get closer to the population mean (μ) (number).

68-95-99.7 Rule

• 68% of data will lie within 1 standard deviation of the mean (σ + μ)
• 95% of data will lie within 2 standard deviations of the mean (2σ + μ)
• 99.7% of data will lie within 3 standard deviations of the mean (3σ + μ)

Sampling Types

Simple Random Sampling (SRS): Normal, random picking.

Systematic Sampling: Every kth sample.

Stratified Sampling: Groups are put together...

Packaging Aesthetics and Local Preferences

Packaging aesthetics are particularly important to the Japanese. Packaging is an important consideration for products that are Japanese prefer plain soft colors on their packages. People have local tastes based on their perceptions and attitudes about a products.

Product Innovation and Branding

Prior to 2004, Nokia launched different cell phone product-communication adaptation. Procter & Gamble recently introduced Pampers Rash Guard, a continuous innovation. Product problems initially policymakers in many parts of the world supported Suzlon. Regulators in different countries have proposed various the use of terms "light" and "natural" are allowed on labels only in the United States. Scotland is a...

What is Statistics?

Statistics is a set of tools designed to analyze data and deduce information about a population from a given sample.

The Three-Step Process of Statistics

1. Sampling and Design of the Experiment: Take a sample (or many) from the population, make observations about the sample, and turn them into numerical data.
2. Descriptive Statistics: Analyze the data to get information about the sample.
3. Statistical Inference: From the data, deduce information about the whole population.

Context is Crucial

The context of a statistical study is crucial in interpreting the results. A population is a set of individuals (people, cases, etc.) that we want to analyze. A sample is a subset of the population. A variable is an aspect or characteristic of the...

Critical Path Method (CPM) vs. PERT

HL (time to completion may be delayed without affecting the beginning of another and final term), HM (the worst case of free float.) Critical path: the path of longer duration and is defined by the sequence of activities that mark critical events in the network. These activities are styled with a double arrow. An activity is critical when it has no slack time, and an event is critical when its TE (earliest time) and TL (latest time) are equal. We must pay critical attention to these routes, as any delay may affect the entire project. Beginning and ending events are critical.

PERT (Program Evaluation Review Technique): It is a probabilistic system that assigns each possible activity three durations: pessimistic,...

Bond Characteristics

• Coupon: The interest payment made by the bond issuer, usually expressed as an annual percentage of the bond's face value.
• Par (Face Value): The amount the bondholder receives when the bond matures, typically $1,000.
• Term to Maturity: The time remaining until the bond's maturity date when the issuer must repay the bond's par value.
• Denomination: The face value of the bond, usually in increments of $1,000.
• Quotation: Bonds are quoted as a percentage of their face value (e.g., a bond quoted at 95 is selling for 95% of $1,000, or $950).

Bond Prices, Yield to Maturity (YTM), Current Yield, and Rate of Return (HPR)

• Bond Prices: The market price of a bond depends on interest rates. Prices and interest rates have an inverse relationship.