GB213 Exam 1

Interval Scale

(I think) Values of a quantitative variable that can be categorized and ranked, and in which differences between values are meaningful.

Width of a class

(Largest value - smallest value)/number of classes

Continuous variable

A variable that assumes uncountable values in an interval

Qualitative variable

A variable that uses labels or names to identify the distinguishing characteristics of observations.

Discrete variable

A variable that assumes a countable number of values

Population parameter

A characteristic of a population

Joint probability Table

A contingency table whose frequencies have been converted to relative frequencies.

Negatively Skewed Distribution of a Histogram

A distribution in which extreme values are concentrated in the left tail of the distribution.

Cumulative Relative Frequency Distribution

A distribution of quantitative data recording the fraction (proportion) of observations that falls below the upper limit of each class.

Relative Frequency Distribution

A frequency distribution that shows the fraction (proportion) of observations in each category of qualitative data or class of quantitative data.

Variable

A general Characteristic of being ovserved on a set of people, objects, or events, where each observation varies in kind or degree

Polygons

A graph of a frequency or relative frequency distribution in which lines connect a series of neighboring points, where each point represents the midpoint of a particular class and its associated frequency or relative frequency.

Ogive

A graph of the cumulative frequency or cumulative relative frequency distribution in which lines connect a series of neighboring points

Bar Chart

A graph that depicts the frequency or relative frequency of each category of qualitative data as a series of horizontal or vertical bars, the lengths of which are proportional to the values that are to depicted.

Histogram

A graphical depiction of a frequency or relative frequency distribution; it is a series of rectangle where the width and height of each rectangle represent the class width and frequency (or relative frequency) of the respective class.

Box Plot

A graphical display of the minimum value, quartiles, and the maximum value of a data set.

Scatterplot

A graphical tool that helps in determining whether or not two variables are related in some systematic way. Each point in the diagram represents a pair of known or observed values of the two variables.

Correlation coefficient

A measure that describes the direction and strength of the linear relationship between two variables

Covariance

A measure that reveals the direction of the linear relationship between two variables.

Probability

A numerical value between 0 and 1 that measures the likelihood that an event occurs.

Symmetry

A plane figure that can be folded along a line so the two parts match.

Classical probability

A probability often used in games of chance. It is based on the assumption that all outcomes are equally likely.

Empirical probability

A probability value based on observing the relative frequency with which an event occurs.

Experiment

A process that leads to one of several possible outcomes

Sample statistic

A random variable used to estimate the unknown population parameter of interest.

Sharpe Ratio

A ratio calculated by dividing the difference of the mean return from the risk-free rate by the asset's standard deviation

Sample Space

A record of all possible outcomes of an experiment

Total Probability Rule

A rule that expresses the unconditional probability of an event in terms of probabilities conditional on various mutually exclusive and exhaustive events.

Pie Chart

A segmented circle portraying the categories and relative sizes of some qualitative variable.

Event

A subset of the sample space

Frequency Distribution

A table that groups qualitative data into categories, or quantitative data into intervals called classes, where the number of observations that fall into each category or class is recorded.

Contingency Table

A table that shows frequencies for two qualitative (categorical) variables, x and y, where each cell represents a mutually exclusive combination of the pair of x and y values.

Quantitative variable

A variable that assumes meaningful numerical values for observations

Stem-and-leaf diagram

A visual method of displaying quantitative data where each value of a data set is separated into two parts: a stem, which consists of the leftmost digits, and a leaf, which consists of the last digit.

The Empirical Rule

Bell shaped distribution, approcimately 68% of all observations fall in the interval +-1s, 95% for +-2, and the rest for +-3

Mutually exclusive

Events that do not share any common outcome of an experiment.

Chebyshev's Theorem

For any data set, the proportion of observations that lie within k standard deviations from the mean is at least 1-1/k^2, where k is any number greater than 1

Law of Large numbers

In probability theory, if an experiment is repeated a large number of times, its empirical probability approaches its classical probability.

Classes

Intervals for a frequency distribution of quantitative data

Mean absolute deviation MAD

The average of the absolute differences between the observations and the mean.

Variance

The average of the squared differences from the mean; a common measure of dispersion

Mean (average)

The average value of a data set

Range

The difference between the max and the min values in a data set

Interquartile Range (IQR)

The difference between the third and first quartiles.

Symmetric Distribution of a Histogram

The graph is symmetric

Mean-variance analysis

The idea that the performance of an asset is measured by its rate of return, and this rate of return is evaluated in terms of its reward (mean) and risk (variance)

Median

The middle value of a data set

Mode

The most frequently occurring value in a data set

Independent Events

The occurrence of one event does not affect the probability of the occurrence of the events.

Dependent events

The occurrence of one event is related to the probability of the occurrence of the other event.

Standard Deviation

The positive square root of the variance; a common measure of dispersion

Conditional probability

The probability of an event given that another event has already occured.

Unconditional probability

The probability of an event without any restriction

The Complement Rule

The probability of the complement of an event is one minus the probability of the event.

Multiplication Rule

The probability that A and B both occur is equal to the probability that A occurs given that B has occurred times the probability that B occurs

Addition Rule

The probability that A or B occurs, or that at least one of these events occurs, is equal to the probability that A occurs, plus the probability that B occurs, minus the probability that both A and B occur.

Percentile

The pth percentile divides a data set into two parts: approximately p percent of the observations have values less than the pth percentile and approximately (100-p) percent of the observations have values greater than the pth percentile.

Coefficient of Variation (CV)

The ration of the standard deviation of a data set to its mean; a relative measure of dispersion.

Z-scores

The relative position of a value within a data set; it is also used to detect outliers.

Bayes' Theorem

The rule for updating probabilities. Assign variables and probabilities to each given variable.

Time series data

Values of a characteristic of a subject over time

Cross-sectional data

Values of a characteristic of many subjects at the same point in time or approximately the same point in time.

Ordinal Data

Values of a qualitative variable that can be categorized and ranked

Nominal Data

Values of a qualitative variable that differ merely by name or label.

Exhaustive event

When all possible outcomes of an experiment are included in the events.

Population

a large set of data; all members of a specific group; the complete collection of items of interest in a statistical problem.

Inferential Statistics

refers to drawing conclusion about a large set of data

Descriptive Statistics

refers to the summary of important aspects of a data set

Sample

smaller set of data; a subset of a particular population;

Positively skewed distribution of a Histogram

the higher ones are to the left (usually bar graph); a distribution in which extreme values are concentrated in the right tail of the distribution