Business Analytics - Descriptive Statistics

pg - 24 - 68

Data

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

Variable

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

Observation

Set of values corresponding to a set of variables

Variation

Dfference in a variable measured over observations

Descriptive analytics

Collect and analyze data to gain a better understanding of variation and its impact on the business setting

Decision variables

The values of some variables are under direct control of the decision maker

Random/Uncertain Variable

Quantity whose values are not known with certainty is called

Population

The set of all elements of interest in a particular study

Sample

Subset of the population

Random sampling

Collecting a sample that ensures that (1) each element selected comes from the same population and (2) each element is selected independently.

Quantitative Data

Data is numeric and arithmetic operations, such as addition, substraction and division can be performed on them.

Categorical Data

If it cannot Arthimetic cannot be applied to them.

Categorical Data

This data is treated through counting the number of observations or computing the proportions of observations in each category

Cross-sectional data

Type of data that is collected from several entities at the same, or approximately the same, point in time.

Time series data

Collected over several periods of time.

Experimental study

Identify the Variable of interest → Using 2 or more Variables to impact the Variable of interest

Non-Experimental/Observational study

Make no attempt to control the variables of interest

Survey

Most common type of observational study.

Distributions

Help summarize many characteristics of a data set by describing how often certain values for a variable appear in that data set.

Distributions

created for both categorical and quantitative data, and they assist the analyst in gauging variation.

Classes

Bins for categorical data

Frequency distribution

Summary of the number that data shows up in observations.

Bin

The nonoverlapping groupings of data

Relative Frequency Distribution

Tabular summary of data showing the relative frequency for each bin.

Percent frequency distribution

Tabular summary of data showing the percent frequency for each bin.

Percent frequency distribution

can be used to provide estimates of the relative likelihoods of different values for a random variable. So

Bin Width

Largest Data Value - Smallest Data Value / No. Of bins

Histogram

Graphical presentation of a frequency distribution, relative frequency distribution, or percent frequency distribution of quantitative data.

Frequency polygon

A chart used to display a distribution by using lines to connect the frequency values of each bin.

Frequency polygon

Comparing distributions, particularly for quantitative variables.

Histogram with Clustered Columns

Frequency Polygon

Histogram

Cumulative frequency distribution

Shows the number of data items with values less than or equal to the upper limit of each bin

Arithmetic Mean

The most commonly used measure of location

measure of central location for the data.

Mean
Median

Median

Value in the middle when the data are arranged in ascending order

Mode

Value that occurs most frequently in a data set

Multimodal

At least two modes

Geometric mean

Measure of location that is calculated by finding the nth root of the product of n values.

Geometric mean

Range

Simplest measure of veriability

Range

Can be found by subtracting the smallest value from the largest value in a data set.

Variance

Measure of variability that utilizes all the data

Variance

Deviation about the mean squared

Deviation

Observation about the mean is written Xi - x̄

Population Variance

can be computed directly rather than using sample variance For a population of N observations

Population Variance

Population Variance

Sample Variance

𝜇

denoting the population mean

Standard Deviation

positive square root of the variance

s

Standard Deviation

𝜎

to denote the population standard deviation.

Coefficient of Variation

Standard deviation/mean * 100%

Percentiles

Value of a variable at which a specified (approximate) percentage of observations are below that value.

Percentile

1. Percentile

2. Find that spot in the set

3. Compute

Steps of Percentile

Q1

First quartile, 25th

Q2

Second quartile, 50th

Q2

Third quartile, 75th

Quartile

It is often desirable to divide data into four parts, with each part containing approximately one-fourth, or 25 percent, of the observations.

Z-score

allows us to measure the relative location of a value in the data set.

Z-score

How far a particular value is from the mean relative to the data set’s standard deviation.

Z-score

standardized value.

Empirical rule

determine the percentage of data values that are within a specified number of standard deviations of the mean.

Approximately 68% of the data

values will be within 1 standard deviation of the mean.

Approximately 95% of the data

values will be within 2 standard deviations of the mean.

Almost all

data values will be within 3 standard deviations of the mean.

Outliers

An unusually large or unusually small data value. - extreme values

Outliers

Above or Below 3

Boxplots

Box-and-whisker plots.a graphical summary of the distribution of data

Outliers

in a boxplot these are extreme values that should be investigated to ensure data accuracy.

Interquartile range

Q3-Q1

Box plot

Upper limit Q3+1.5(IQR)

Box plot

Lower limit Q1-1.5(IQR)