Data Science Final Exam Review Flashcards

Comprehensive review flashcards covering Python data types, Table operations, visualization techniques, statistical concepts, and hypothesis testing based on the final lecture transcript.

% (Modulo Operator)

A special expression in Python that returns the remainder from division.

** (Exponent Operator)

A special expression in Python that returns the first number raised to the power of the second number.

Integers (int)

Whole numbers of any size (e.g., $1$, $3$, $5$) that never have a decimal point in Python.

Floats (float)

Numbers with an optional fractional part (decimal) that have a limited precision of $15$-$16$ decimal places.

Strings

A data type consisting of a series of characters surrounded by quotation marks, such as "Hello, world!", 'eight', or '10'.

Arrays

A sequence of values where all elements should have the same data type and arithmetic is applied to each element individually.

Ranges

An array of consecutive numbers created using functions like $np.arange(start, end, step)$ which always include the start but exclude the end.

Lists

Created with square brackets $[]$, these can contain mixed data types and are commonly used to group by multiple columns in Tables.

Booleans

A data type with two possible values, $True$ or $False$, often used in functions or as the output of comparison statements.

Table

A sequence of labeled columns where each row represents one individual and columns represent attributes.

t.select(label)

A table operation that constructs a new table containing only the specified columns.

t.drop(label)

A table operation that constructs a new table in which the specified columns are omitted.

t.where(label, condition)

A table operation that constructs a new table with just the rows that match a specific condition.

t.column(label)

An operation that pulls a column out of a table as an array of its values.

apply()

A method that creates an array by calling a specific function on every element in one or more input columns.

Pivoting

Converting a table from long form to wide form to cross-classify according to two categorical variables, producing a grid of counts or aggregated values.

Joining/Merging

The process of combining tables using the $.join()$ method; rows are dropped if values in the common column are not present in both tables.

Scatter plot

A visualization produced by $t.scatter()$ that shows the relationship between two quantitative (numerical) variables.

Line plot

A visualization produced by $t.plot()$ that is useful for plotting trends of a numerical variable over a sequential variable like time.

Bar charts

A visualization produced by $t.barh()$ used to display the distribution of a categorical variable.

Histogram

A chart that displays the distribution of a numerical variable using bins, where height represents density and area represents percent.

Histogram Height Formula

$$Height = \frac{\% \text{ in bin}}{\text{width of bin}}$$

Histogram Area

$$Area \text{ of bar} = \% \text{ in bin} = Height \times \text{width of bin}$$

Addition Rule (OR)

If event $A$ can happen in exactly one of two ways, then $P(A) = P(\text{first way}) + P(\text{second way})$.

Multiplication Rule (AND)

The chance that two events $A$ and $B$ both happen in order: $P(A \text{ happens}) \times P(B \text{ happens given that } A \text{ has happened})$.

Systematic sample

A sampling method where subjects are lined up in order and every nth subject is sampled.

Deterministic sample

A sampling scheme where the procedure is set by the researcher and does not involve chance.

Random sample

A sample where individuals are drawn at chance equal to their proportion in the population, requiring known selection probabilities.

Empirical Distribution

A distribution based on observations from repetitions of an experiment or simulated observations.

Probability Distribution

A theoretical distribution that mathematically describes all possible values of a quantity and their true probabilities.

Parameter

A "true" number associated with the total population, such as the true average height of all college students.

Statistic

A number calculated from a sample (e.g., sample average) used as an estimate of a parameter.

Confounding Variables

A hidden, external factor that influences both independent and dependent variables, creating misleading associations.

Observational Study

A study that involves passively watching and measuring variables as they naturally occur, revealing associations but not causation.

Experiment

A study where the researcher actively applies a treatment to different groups, often through random assignment, to establish cause-and-effect.

Null Hypothesis ($H_0$)

A well-defined probability model about how data were generated, where small differences are attributed to random chance.

Alternative Hypothesis ($H_a$)

A different view about the origin of data suggesting that observed data are not consistent with the null model.

Bootstrapping

A resampling technique where new samples of the same size as the original are drawn at random with replacement to estimate population parameters.

Confidence Interval

An interval of estimates of a parameter; for example, a $95\%$ interval shows the middle $95\%$ of the bootstrapped data.

P-value

The probability of obtaining a result as extreme as, or more extreme than, the one actually observed, assuming the null hypothesis is true.

Statistically Significant

A result where the p-value is less than $0.05$, suggesting the data supports the alternative hypothesis over the null.

Central Limit Theorem

The principle that the probability distribution of the sum or mean of a large random sample drawn with replacement will be roughly normal.

Normal Distribution Rule

In a bell-shaped curve, $68\%$ of observations are within $1$ SD of the mean, $95\%$ within $2$ SD, and approximately $99\%$ within $3$ SD.

Z-Scores

A measure used to find how many standard deviations an observation is from the mean, helping to standardize comparisons and identify outliers.