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• Chapter 3 explores basic statistics and tools for business analytics.
• Chapter 3 includes distinguishing populations from samples, sampling methods, bias in business analytics and basic statistics.
• Chapter 3 also covers software tools such as Excel and Tableau to visualize statistics using histograms and box plots and to perform correlation and regression analysis.

Population vs. Sample

• A population is a group with shared characteristics, which may be impossible or expensive to fully survey.
• A parameter is a characteristic of a population.
• A sample is a representative subset of a population.
• A statistic is a characteristic of a sample, from which inferences about the population can be drawn.
• Descriptive statistics measures the data of a population or sample.
• Inferential statistics is used to arrive at conclusions about a population using only sample data.
• A hypothesis is a proposed explanation based on limited evidence, used as a starting point for further investigation, using inferential statistics.

Sampling Methods

• Simple random sampling is one way to choose a representative sample.
• Stratified random sampling includes all groups or strata.
• Cluster sampling selects a few groups or clusters.
• Convenience sampling is non-probability sampling.

Data Reduction

• Data Reduction reduces the size of a dataset to a manageable size for business analysis projects by focusing on critical, interesting, or abnormal items which can speed up analysis and reduce costs.
• Filtering is a common data reduction method.

Bias in Business Analytics

• Prejudice in favor of or against a thing, person, or group is considered bias.
• Types of bias include nonresponse, selection, confirmation, and outlier bias.
• Bias can be intentional or unintentional and occur during data collection, analysis, or when presenting the results.

Probability Distributions

• A random variable quantifies the outcomes of random occurrences.
• Data distribution displays possible values for a variable and how often they occur.
• Probability distribution is a statistical function.
• Probability distributions can describe possible population values and the likelihood of observations (random variables) taking a value.

Types of Numerical Data

• Continuous data includes any numerical value, including non-whole numbers.
• Continuous data uses an infinite set of values between observations.
• Examples of Continuous data include height, weight, and currency.
• Discrete data only consists of whole numbers (integers).
• Discrete data uses a finite set of values between observations.
• Examples of discrete data: inventory, vehicles, and manufacturing plants.

Measures of Central Tendency

• Measures of central tendency describe the center point of a data set.
• Mean is the average, calculated as the sum of values divided by the number of values (Sum/n).
• Median is the midpoint of a data distribution.
• Mode is the most common observation in a dataset.
• Kurtosis is the distribution shape in tails.
• Symmetry refers to when the Mean, Median, and Mode are equivalent.

Skewness

• In right-skewed distributions, also known as positive skewness, the mean is higher than the median and mode.
• In left-skewed distributions, also known as negative skewness, the mean is lower than the median and mode.

Measures of Dispersion

• Measures of dispersion describe how dispersed a dataset is.
• Range = Maximum - Minimum
• Interquartile Range is comprised of 4 quartiles.
• Variance is the average of squared deviations from the mean.
• Standard Deviation is the square root of the variance and uses the same units as the data values.

Continuous Probability Distributions

• Z-score is the number of standard deviations a data point is from the mean, calculated as: )/standard deviation. Mean = Median = Mode = 0
• Standard deviation = 1
• The special case of normal distribution uses theoretical distributions.
• The special case involves comparisons and calculates probabilities of individual observations.

Calculating Summary Statistics

• Excel, Power BI, and Tableau are software packages for data analysis

Frequency Distribution

• Frequency Distribution requires numerical data.
• Frequency Distribution uses Bins, classes, and intervals which are categories in numerical data.
• Frequency Distribution is a table which uses bins or categories to list the frequency of various sample outcomes.
• Visual representations of frequency distribution include Histograms.

Confidence Interval

• Point Estimate is a single value to estimate a population parameter but Point Estimate can be difficult to be accurate.
• Confidence Interval is a range of numbers at a certain Confidence Level around the point estimate.
• Level of Confidence is a probability that the Population parameter falls within a range.
• Confidence Interval = Point estimate +/- Margin of Error
• Confidence Interval = Lower bound < population parameter < upper bound
• Confidence Interval is a function of desired Confidence Level plus Standard Error. Confidence Interval error reflects inability to capture true population parameter.

Hypothesis Testing

• Hypothesis consists of proposed explanations.
• Hypothesis Test determines if statistically significant differences exist between groups.
• Significant or Not Random or by chance
• Two-tailed: different?
• One-tailed: direction of difference?

Hypothesis Testing - Steps

1. Determine Hypotheses
2. Set the Statistical Significance (Alpha, α)
3. Calculate the Test Statistic
4. Reject or Fail to Reject the Null Hypothesis Using p-value

• Null Hypothesis (Ho)=Base case being tested, no relationship, not reject/reject
• Alternative Hypothesis (H₂) = Tested against Ho, expected relationship
• It is assumed to be true if Ho is rejected

Correlation

• Correlation measures the linear association, or the relationships between two variables.
• With correlation, examine how the variables change with respect to each other.
• Variable is a measurement that changes over time or between individuals/subjects.
• Excel Data > Analysis > Data Analysis> Correlation calculates a Correlation Coefficient

Correlation Coefficient

• Correlation Coefficient = 0 means No relationship exists.
• Correlation Coefficient = -1 means perfectly negatively correlated.
• Correlation Coefficient = 1 means perfectly positively correlated.

Linear Regression Analysis

• Linear Regression Analysis calculates an equation y = mx + b.
• y = dependent variable you are predicting
• x = independent variable help explains
• m = slope of the line, steepness and direction
• b = intercept = where line starts at Y-axis
• Linear Regression Analysis Measures the relationship between one output variable (y) and one or more input variables (x).
• Linear Regression Analysis predicts the dependent variable. -Simple form is one independent variable (x) . -Multiple is more than one independent variable (x) -Line of best fit is the regression model that best expresses the relationship between data points