Business Analytics Chapter 2

Geometric Mean

nth root of the product of n values -Used in analyzing growth rates in financial data.

Quantitative data

Data on which numeric and arithmetic operations, such as addition, subtraction, multiplication, and division, can be performed

Standard Deviation

Positive square root of the variance -measures in the same unity as the original data

Observation

Set of values corresponding to a set of variables

Variation

The difference in a variable measured over observations

Data

The facts and figures collected, analyzed, and summarized for presentation and interpretation.

Coefficient of Variation

(Standard Deviation/Mean *100) -Measures the standard deviation relative to the mean -expresses as a percentage.

Population

All elements of interest

Experimental

Experimental Study: A variable of interest is first identified-then one or more other variables are identified and controlled or manipulated so that data can be obtained about how they influence the variable interest.

Outlier:

Extreme Value is a data set -It can be identified using STDV values (z-scores) -Any data value with a z-score less than -3 or greaterthan +3 is an outlier.

No Linear relationship

Near 0

Sample

Subset of the population

Percent frequency Distribution

Summarizes the percent frequency of the data for each bin -Percent frequency distribution is used to provide estimates of the relative likelihoods of different values of random variable.

Scatter Charts:

Useful graph for analyzing the relationship between two variables.

Categorical data

Data on which arithmetic operations cannot be performed

Three steps necessary to define the classes for a frequency distribution with quantitative data:

-Determine the number of nonoverlapping bins -Determine the width of each bin -Determine the bin limits

Variance

-Measure of the variability that utilizes all the data -It is based on the deviation about the mean, which is the difference between the value o each observation (xi) and the mean

Negative Linear

<0

Positive Linear

>0

Variable

A characteristic or quantity or interest that can take on different values

Histogram

A common graphical presentation of quantitative data -Constructed by placing the variable of interest on the horizontal axis and the selected frequency measure (absolute frequency, relative frequency, or precent frequency) on the vertical axis. -the frequency measure of each class is shown by drawing a rectangle whose base is determined by the class limits on the horizontal axis and whose height is the corresponding frequency measure. Provide information about the shape, or form, of a distribution

Random Variable/uncertain variable

A quantity whose values are not known with certainty

Random Sampling

A sampling method to gather a representative sample of the population data.

Frequency distribution

A summary of data that shows the number(frequency) of observation in each of several non-overlapping classes-typically referred to as bins, when dealing with distributions.

Cumulative Frequency Distribution

A variation of the frequency distribution that provides another tabular summary of quantitative data. -uses the number of classes, class widths, and class limits developed for the frequency distribution. -Shows the number of data items with values less than or equal to the upper class limit of each class

Mean/Arithmetic Mean

Average value for a variable -Denoted by x with a line above it. -n=sample size

Cross-Sectional data

Data collected from several entities at the same, or approximately the same, point in time.

Time series data

Data collected over several time periods -Graphs of time series data are frequently found in business and economic publications -Graphs help analysts understand what happened in the past, identify trends over time, and project future level for the time series.

Multimode Data

Data contain at least two modes

Bimodal Data

Data contain exactly two modes

Covariance:

Descriptive measure of the linear association between two variables

Q1

First Quartile: 25th Percentile

Empirical Rule

For data having a bell shaped distribution: Within 1 STDV-approximately 68% of the data values Within 2 STDV- approximately 95% of the data values Within 3 STDV- almost all the data values

Range

Found by subtracting the smallest value from the largest value in a data set Drawback- Range is based on only two of the observations and thus is highly influences by extreme values.

Box Plots

Graphical Summary of the Distribution of Data -Developed from the quartiles for a data set.

Relative Frequency Distribution

It is a tabular summary of data showing the relative frequency for each bin.

Skewness

Lack of Symmetry

Nonexperimental study or observational study

Make no attempt to control the variable of interest -A survey is perhaps the most common type of observation study.

Z-Score

Measures the Relative Location of a value in the data set -Helps to determine how far a particular value is from the mean relative to the data set's standard deviation.

Correlation coefficient:

Measures the relationship between two variables.

Q3

Third quartile: or 75th percentile.

Median

Value in the middle when the data are arranged in ascendin order -middle value, for an odd number of obervations -Average of two omiddle values, for an even number of obervations.

Percentiles

Value of a Variable at which a specified percentage of observations are below that value

Mode

Value that occurs most frequently in a data set

Quartiles

When the data is divided into four equal parts:Each part contains approximately 25% of the observations-Division points are referred to as quartiles

Q2

second quartile: 50th percentile (median)