Business Statistics Unit 1

What is statistics?

the science that deals with the collection, preparation, analysis, presentation, and interpretation of data

Descriptive Statistics

refers to the summary of important aspects of a data set

• Includes collecting, organizing, and presenting the data in the form of charts

and tables

• Often calculate numerical measures (typical value, variabiliy)

Inferential Statistics

refers to drawing conclusions about a larger set of data (population) based on a smaller set of data (sample).

Population

consists of all items/members of interest

Sample

A sample is a subset of population

Need for Sampling

to make inferences about various characteristics of the population.

Cross Sectional Data

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

Time Series Data

refers to data collected over several time periods focusing on certain groups of people, specific events, or objects.

• can include hourly, daily, weekly, monthly, quarterly, or annual observations

Structured Data

• Reside in a pre-defined, row-column format.

• Spreadsheet or database applications.

• Enter, store, query, and analyze.

• Numerical information that is objective and not open to interpretatio

Unstructered Data

• Do not conform to a pre-defined, row-column format.

• Textual and multimedia content.

• Do not conform to database structures.

• These data may have some implied structure.

• Do not conform to a row-column model required in most database systems

Big Data

• A massive volume of structured and unstructured data.

• Extremely difficult to manage, process, and analyze using traditional data processing tools.

• Presents great opportunities to gain knowledge and game-changing intelligence

Qualitative variables

• Also called Categorical Data.

• Represent categories.

• Labels or names to identify distinguishing characteristics.

• Can be defined by two or more categories.

• Coded into numbers for data processing

Quantitative variables

• Also called Numeric Data.

• Represent meaningful numbers.

• Either discrete or continuou

Nominal

• Least sophisticated.

• Represent categories or groups.

• Values differ by label or name.

• Example: marital status

Ordinal

• Stronger level of measurement.

• Categorize and rank data with respect to some characteristic.

• Cannot interpret the difference between the ranked values, numbers are arbitrar

Interval

• Categorize and rank, differences are meaningful.

• Zero value is arbitrary and does not reflect absence of characteristic.

• Ratios are not meaningful

Ratio

• Strongest level of measurement.

• A true zero point, reflects absence of characteristic.

• Ratios are meaningful

Inspecting and preparing the data for analysis

• Counting and sorting.

• Handling missing values.

• Subsetting

Frequency Distribution for Qualitative data

Frequency Distribution for Quantitative data

Constructing a frequency distribution for a numerical variable

details about classes and observations

Relative Frequency

proportion of items

Percent Frequencies

percentage of items

Pie Charts (uses)

a segmented circle whose segments portray the relative frequencies of the categories of a qualitative variable

Bar Charts

depicts the frequency or relative frequency for each category of the categorial variable

Series of either horizontal or vertical bar

bar lengths proportional to the values they are depicting

Histogram

the numerical variable counterpart to the vertical bar chart for a categorical variable

provides information on the shape of the distribution

Ogive

a cumulative frequency polygon or line graph used in statistics to show how many data values lie above or below a specific value

Polygon

a line graph that shows data distribution by connecting the midpoints of the tops of the bars

Scatterplots Positive Linear

displays two quantitative variables that increase together

Scatterplots Negative Linear

displays data points that slope downward from left to right. As the x-value increases, the y-value decreases in a straight-line pattern

Scatterplots Curvilinear

displays data points that follow a smooth curved pattern rather than a straight line, showing that two variables change together at a changing rate instead of a constant one

Scatterplots No Relationship

shows a random spread of dots with no upward trend, downward trend, or clear pattern

Arithmetic Mean Median

• Add all numbers together.

• Divide the total by how many numbers exist.

• Effect: It is easily skewed by very large or very small numbers (outliers

Arithmetic Mean Average

• Sort all numbers from least to greatest.

• Pick the exact middle number.

• If there is an even count of numbers, take the arithmetic mean of the two middle numbers.

• Effect: It resists being skewed by extreme high or low values

Median

The middle point of a data set

Mode

The most frequent value in a data set; how many can be in a data se

Boxplot 5 value

Minimum, Quartile 1, Median, Quartile 3, Maximu

Interquartile Range

Quartile 3 minus Quartile 1

Percentiles

divides a variable into two parts

a technical measure of location and relative position

Geometric mean: the characteristics; when it is useful

measures the rate of change of a variable over time.

smaller than the arithmetic mean

less sensitive to outliers

relevant measure when evaluating investment returns over several years and calculating compoud growth rates

Variance and Standard Deviatio

Most widely used measures of dispersion

Square root of Variance =

Standard Deviation

Coefficient of Variation

A relative measure of dispersion.

Calculated as Std.

Dev. divided by the Mean

Chebyshev’s Theorem

applies to any data shape

Empirical Rule

applies to relatively symmetric and bell shaped date

Analysis of relative location (what capabilities does it provide; what statements does it make)

defines a place or data point by its spatial relationship to other areas, providing context on connectivity, accessibility, and economic potential

Covariance

Measures the direction of the linear relationship between two variables

Correlation coefficient shows

the direction and the strength of the linear relationship between two variables

Correlation coefficient values fall between

-1 (negative relationship) +1 (positive relationship), and 0 (no relation)

Correlation coefficient calculated as

the Covariance of two variables divided by the product of their Standard Deviation