Statistics helps us make sense of data in business. Descriptive stats summarize what we have, like average sales or market share. They give us a snapshot of our current situation.

Inferential stats let us make educated guesses about bigger trends. We can estimate future sales or test if a new strategy really works. This helps us make smarter decisions for our business.

Understanding Descriptive and Inferential Statistics

Descriptive vs inferential statistics

• Descriptive statistics summarize and describe the main features of a dataset, focusing solely on the sample data at hand
• Inferential statistics make generalizations or draw conclusions about a larger population based on the information gathered from a sample

Purpose of descriptive statistics

• Provide a concise summary of a dataset by measuring central tendency
  • Calculate the mean to determine the average value of the dataset
  • Find the median to identify the middle value when the data is ordered from lowest to highest
  • Determine the mode to find the most frequently occurring value in the dataset
• Measure dispersion to understand the spread of the data
  • Calculate the range by finding the difference between the maximum and minimum values in the dataset
  • Compute the variance, which is the average of the squared deviations from the mean ($\sigma^2$ for population, $s^2$ for sample)
  • Find the standard deviation by taking the square root of the variance ($\sigma$ for population, $s$ for sample)
• Visualize data to identify patterns and trends
  • Create graphs such as bar charts (categorical data), histograms (continuous data), or pie charts (proportions)
  • Construct tables like frequency tables (data distribution) or contingency tables (relationship between variables)

Role of inferential statistics

• Estimate population parameters based on sample statistics
  • Use point estimation to provide a single value estimate of a population parameter (sample mean)
  • Calculate interval estimation to determine a range of values likely to contain the population parameter (confidence intervals)
• Test hypotheses about population parameters
  • State the null hypothesis ($H_0$) as a claim of no effect or no difference (no correlation between variables)
  • Formulate the alternative hypothesis ($H_a$ or $H_1$) as a statement contradicting the null hypothesis (correlation exists)
  • Calculate the p-value, which is the probability of obtaining the observed results or more extreme results, assuming the null hypothesis is true
  • Set the significance level ($\alpha$), typically at 0.05, as the threshold for rejecting the null hypothesis

Statistical techniques in business

• Apply descriptive techniques to summarize business data
  • Calculate summary statistics like mean (average sales), median (middle salary), or standard deviation (variability in profits)
  • Create data visualizations such as bar charts (product categories) or pie charts (market share)
• Use inferential techniques to make data-driven business decisions
  • Construct confidence intervals to estimate population parameters (average customer spend)
  • Conduct hypothesis tests to make claims about population parameters
    1. Perform t-tests to compare means between groups (customer satisfaction scores) or to a known value (industry benchmark)
    2. Use ANOVA to compare means across multiple groups (sales performance by region)
    3. Apply chi-square tests to examine relationships between categorical variables (gender and purchasing behavior)
  • Employ regression analysis to model relationships between variables
    • Utilize simple linear regression to predict an outcome based on one predictor variable (sales based on advertising spend)
    • Apply multiple linear regression to predict an outcome based on multiple predictor variables (customer loyalty based on price, quality, and service)