ST 113 Exam 1 (Ch 1-3)

Chebyshev's Theorem

1-1/k^2 applicable to any distribution

Empirical Rule

68%, 95%, 99.7% given sample mean, standard deviation and a symmetric bell-shaped distribution

(Population) Parameter

A value that describes or summarizes a given aspect of a population.

Data

a compilation of fact, figures, or other content, both numerical and nonnumerical.

Line Chart

a graph that connects consecutive observations of a numerical variable with a line. it tends to be used to track changes of the variable over time.

Percentile

a measure of central location also used to measure relative position.

Covariance

a measure of the direction of linear association between two variables (<0 negative/inverse relationship, >0 positive/direct relationship, =0 no relationship)

Histogram

a series of rectangles where the width and height of each rectangle represents the width and frequency of the respective class.

Sample

a subset of the population. - an observation is a single item in a sample - a census is a sample consisting of the entire population

z-score

a unit less measure, measures the distance of an observation from the mean in terms of standard deviation. method for standardizing observations from variables with different means and standard deviations.

(Sample) Statistic

a value that describes or summarizes a given aspect of a sample.

Population

all members of a specified group being researched or investigated.

Data Set

all the data collected to analyze a particular question or topic.

Variables

an observable characteristic that varies across individuals or time in the population. two types: categorical (qualitative), numerical (quantitative)

Sharpe Ratio

characterizes how well an asset's return compensates for the risk of an investment.

Central Location

concept that captures the manner in which data observations tend to cluster around some middle value. represents some "typical" or "central value" that describes the variable. three measures (mean, median, and mode)

Polygon

connected series of neighboring points where each point represents the mid-point of a particular class and its associated frequency or relative frequency.

Ogive

connected series of neighboring points where each point represents the upper limit of a particular class and its associated cumulative frequency or cumulative relative frequency.

Stem and Leaf Diagram

constructed by separating each observation of a numerical variable into two parts: a stem, consisting of the leftmost digits, and a leaf, consisting of the last digits. convey similar information as a histogram. provide an overall visual display of where observations are centered and how they are dispersed around the center.

Time-Series Data

data collected over several regularly spaced time periods, focusing on a certain group of people, specific events or objects. time series dimensions: by minute, hour, daily, weekly, monthly, yearly etc.

Cross-Sectional Data

data collected without recording a characteristic of many subjects at the same point in time or without regard to differences in time.

Positively (right) Skewed Distribution

distribution exhibiting the presence of a small number of relatively large observations from the center of the distribution.

Negatively (left) Skewed Distribution

distribution exhibiting the presence of a small number of relatively small observations from the center of the distribution.

Cumulative Relative Frequency

distribution that records the proportion of observations that fall below the upper limit of a particular class.

Scatterplot

graphical tool that aids in the determination of whether two numerical variables are systematically related. each point represents a pair of observations of the two variables. reveals direction, shape, and strength of the relationship between variables.

Small values of standard deviation

indicate less dispersion around the mean

Large values of standard deviation

indicate more dispersion around the mean

Nominal Scale

least sophisticated level of measurement, can only be grouped or categorized, variables only differ by name or label.

Coefficient of Variation (CV)

measure of dispersion that is comparable across variables with different units or mean (standard deviation/mean)

Range

measures the difference between the maximum and minimum values of a variable in a sample or population. (weakness is based only on extreme values of a variable)

Correlation Coefficient

measures the direction and strength of linear association between two variables (-1 negative linear relationship, 1 positive linear relationship, 0 no linear relationship) (strong 0.70, moderate 0.30-0.70, weak 0-0.30)

Mean-Variance Analysis

methodology that postulates 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). in general higher avg returns are associated with higher risk.

Median

middle observation in a sample or population after arranging variables in order of smallest to largest

Mode

most frequently occurring observation in a sample or population. only meaningful measure of central location for categorical variables. (variable may have none or more than one)

Mean

most utilized measure of central location. the sum of all the population or sample observations of a variable divided by the number of observations. (weakness of outliers)

Descriptive Statistics

refers to the summary of important aspects of a data set. data production: collecting data samples and collecting data from experiments data analysis: organizing, summarizing, describing, and presenting data

Variance/Standard Deviation

squares the deviations from the mean to eliminate the summing to zero effect and computes the average of the squared deviations. (measure of risk)

Ordinal Scale

stronger measurement level than nominal, variables can be categorized and ranked with respect to some characteristic or trait. cannot interpret the difference between ranked characteristics or traits.

Interval Scale

stronger measurement level than ordinal, can be categorized, ranked with respect to some characteristic or trait, and find meaningful differences between scales. value of zero is arbitrary.

Ratio Scale

strongest measurement level, can be categorized, ranked with respect to some characteristic or trait, find meaningful differences between scales, and has a meaningful zero point (interpretable)

Mean Absolute Deviation (MAD)

the average absolute deviation from the mean

Weighted Mean

the mean obtained by assigning each observation a weight that reflects its importance. (wi*xi)

Relative Frequency

the proportion of observations in a category.

What is statistics?

the science concerned with developing and studying methods for collecting, analyzing, interpreting and presenting empirical data.

Inerential Statistics

using sample data (descriptive statistics) to draw conclusions about a population on which the sample is based.

Continuous Variable

variable categorized by uncountable values contained within an interval.

Discrete Variable

variable taking on a countable number of values.

Sample Mean

x̅ , called a statistic

Population Mean

μ , called a parameter