Probs and Statistics Review Flashcards

Comprehensive practice questions covering basic numeracy, arithmetic, fractions, algebra, descriptive statistics, correlation, regression, and probability based on the module lecture notes.

How do whole numbers differ from integers?

Both numerical systems consist of figures without fractional or decimal components, but while whole numbers are non-negative ($0, 1, 2, ...$), integers can be positive, negative, or zero.

What is the definition of a rational number?

A number that can be expressed as a fraction ($\frac{a}{b}$), including all integers and decimals that either terminate or repeat indefinitely.

How is a continuous set of data distinguished from a discrete set?

A discrete set contains unconnected points or distinct values that are counted (e.g., number of cars), while a continuous set can hold any value within an interval and is often measured (e.g., age or temperature).

What mathematical property states that adding $0$ to any number does not change the original number?

The identity property, denoted as $a + 0 = a$.

In the order of operations, what does the acronym PEMDAS stand for?

Parentheses, Exponents (and roots), Multiplication and Division (from left to right), Addition and Subtraction (from left to right).

What is the difference between a prime number and a composite number?

A prime number is a positive integer with exactly two factors ($1$ and itself), whereas a composite number has at least one positive factor other than $1$ and itself.

According to the Fundamental Theorem of Arithmetic, every composite number is what?

The product of a unique set of prime numbers.

How do you calculate the Greatest Common Factor (GCF) of two numbers?

By identifying all factors of each integer and determining the largest factor that both numbers have in common.

Define a proper fraction, an improper fraction, and a mixed number.

Proper: numerator is less than denominator ($< 1$); Improper: numerator is greater than or equal to denominator ($> 1$); Mixed: consists of a whole number and a proper fraction.

What is the 'Butterfly Method' used for in the context of fractions?

A method of cross-multiplication used to determine if two fractions or proportions are equivalent.

What are the common household conversion rates for volume mentioned in the notes?

$1\,\text{tablespoon} = 3\,\text{teaspoons}$, $1\,\text{fluid ounce} = 2\,\text{tablespoons}$, $1\,\text{cup} = 8\,\text{fluid ounces}$, and $1\,\text{gallon} = 4\,\text{quarts}$.

What are the formulas for converting between Fahrenheit and Celsius?

$F = C \times \frac{9}{5} + 32$ and $C = (F - 32) \times \frac{5}{9}$.

What is a 'coefficient' in an algebraic expression?

A constant number by which a variable is multiplied, written directly in front of the variable (e.g., $16$ in $16x$).

What occurs when you multiply or divide both sides of a linear inequality by a negative number?

You must switch the direction of the inequality sign ($<$ becomes $>$).

Define the slope of a line and its algebraic formula.

The pitch or tilt of a line, calculated as $\frac{\text{rise}}{\text{run}}$ or $\frac{y_2 - y_1}{x_2 - x_1}$ using two coordinates $(x_1, y_1)$ and $(x_2, y_2)$.

What are the characteristics of a 'normal distribution' regarding the Standard Deviation Rule?

Approximately $68\%$ of data falls within $1$ standard deviation of the mean, $95\%$ within $2$ standard deviations, and $99.7\%$ within $3$ standard deviations.

What is the '1.5 IQR Criterion' used for in statistics?

To identify outliers; any point more than $1.5 \times \text{IQR}$ above the third quartile ($Q_3$) or below the first quartile ($Q_1$) is considered an outlier.

How do you distinguish between quantitative and categorical data?

Quantitative (numerical) data consists of counts or measurements, while categorical (qualitative) data consists of groups, names, or labels.

Which measure of center is preferred for skewed data and why?

The median, because it is a resistant measure that is not substantially influenced by extreme values or outliers, unlike the mean.

What is the five-number summary used to create box plots?

Minimum, First Quartile ($Q_1$), Median ($Q_2$), Third Quartile ($Q_3$), and Maximum.

Define explanatory and response variables.

An explanatory variable (independent, $x$) is the suspected cause or used for prediction, while the response variable (dependent, $y$) is the affected variable or measured effect.

What is the correlation coefficient ($r$) and what range of values can it take?

A measure of the strength and direction of a linear relationship between two quantitative variables, ranging from $-1$ to $+1$.

Distinguish between a stratified sample and a cluster sample.

A stratified sample involves breaking the population into distinct categories and sampling from each, while a cluster sample involves selecting random groups or chunks of the population and gathering data from all units within those clusters.

What is Simpson's Paradox?

A counterintuitive situation where a trend appearing in separate groups of data disappears or even reverses when the groups are combined, typically caused by a lurking variable.

Differentiate between linear interpolation and linear extrapolation.

Interpolation is making a prediction within the range of known data points, while extrapolation is making a prediction outside the range of known data points, which is generally less reliable.

Define 'independent events' in probability.

Events where the occurrence of one does not affect the probability that the other will occur.

What is the General Addition Rule for probability?

$P(A\,or\,B) = P(A) + P(B) - P(A\,and\,B)$, used to find the probability of at least one event occurring.

What is the Law of Large Numbers?

A principle stating that as the number of trials increases, the relative frequency of an event will converge on its theoretical probability.

How is conditional probability denoted and what is its formula?

It is denoted as $P(B|A)$, read as 'probability of B given A,' and calculated as $\frac{P(A\,and\,B)}{P(A)}$.

What defines 'disjoint events' in a Venn diagram?

Events that have no intersection ($P(A\,and\,B) = 0$), meaning they cannot both occur at the same time.