Business Analytics 101: Exploratory Data Analysis Descriptive Statistics Mean Median Mode Range Variance Standard Deviation Skewness Kurtosis

What This Is

Descriptive statistics is a branch of statistics that deals with summarizing and describing the basic features of a dataset. It provides a way to understand the distribution of data, identify patterns, and make informed decisions. In business analytics, descriptive statistics is crucial for tasks such as forecasting sales, segmenting customers, detecting fraud, and evaluating the performance of a company. For instance, a retail company might use descriptive statistics to analyze customer purchase behavior, identify trends, and optimize marketing strategies.

Key Formulas & Metrics

• Mean = (Σxᵢ) / n – average value of the dataset, where xᵢ represents individual data points and n is the total number of data points.
• Median = (n + 1)th data point when n is odd, or (n / 2)th data point + ((n / 2 + 1)th data point) / 2 when n is even – middle value of the dataset when it is sorted in ascending order.
• Mode = most frequently occurring value – value that appears most often in the dataset.
• Range = Maximum value - Minimum value – difference between the largest and smallest values in the dataset.
• Variance = Σ(xᵢ - Mean)² / (n - 1) – measure of spread or dispersion of the dataset.
• Standard Deviation = √Variance – square root of the variance, representing the average distance of data points from the mean.
• Skewness = (Σ(xᵢ - Mean)³ / (n - 1)) / (Standard Deviation)³ – measure of asymmetry of the dataset.
• Kurtosis = (Σ(xᵢ - Mean)⁴ / (n - 1)) / (Standard Deviation)⁴ - 3 – measure of the "tailedness" or "peakedness" of the dataset.

Step-by-Step Procedure

1. Collect and clean the data: Gather the relevant data and ensure it is free from errors and inconsistencies.
2. Compute the mean: Calculate the average value of the dataset using the formula Mean = (Σxᵢ) / n.
3. Compute the median: Find the middle value of the dataset when it is sorted in ascending order.
4. Compute the mode: Identify the most frequently occurring value in the dataset.
5. Compute the range: Calculate the difference between the largest and smallest values in the dataset.
6. Compute the variance and standard deviation: Use the formulas Variance = Σ(xᵢ - Mean)² / (n - 1) and Standard Deviation = √Variance to calculate the spread of the dataset.
7. Compute skewness and kurtosis: Use the formulas Skewness = (Σ(xᵢ - Mean)³ / (n - 1)) / (Standard Deviation)³ and Kurtosis = (Σ(xᵢ - Mean)⁴ / (n - 1)) / (Standard Deviation)⁴ - 3 to assess the asymmetry and "tailedness" of the dataset.

Common Mistakes

• Mistake: Confusing correlation with causation.
• Correction: Correlation does not imply causation. A strong correlation between two variables does not necessarily mean that one variable causes the other.
• Mistake: Misinterpreting p-values.
• Correction: A p-value represents the probability of observing the data (or more extreme) if the null hypothesis is true. It does not provide information about the probability of the null hypothesis being true.
• Mistake: Using the wrong error metric for a business problem.
• Correction: Choose an error metric that aligns with the business objective. For example, use mean absolute error (MAE) for forecasting tasks and mean squared error (MSE) for regression tasks.

Software / Tool Tips

• Python with pandas and scikit-learn: Use the mean(), median(), mode(), var(), std(), skew(), and kurtosis() functions from the pandas library to compute descriptive statistics. Use the describe() function to get a summary of the dataset.
• R: Use the mean(), median(), mode(), var(), sd(), skewness(), and kurtosis() functions from the stats package to compute descriptive statistics. Use the summary() function to get a summary of the dataset.
• Excel: Use the AVERAGE(), MEDIAN(), MODE.SNGL(), VAR.S(), STDEV.S(), SKEW(), and KURT() functions to compute descriptive statistics.

Quick Practice Problem

Scenario: A company wants to analyze the sales of its products over the past year. The sales data is as follows: 100, 110, 105, 120, 115. What does an R² of 0.85 mean?

Answer: An R² of 0.85 means that 85% of the variation in sales can be explained by the independent variable(s) in the regression model.

Last-Minute Cram Sheet

1. Mean = (Σxᵢ) / n – average value of the dataset.
2. Median = (n + 1)th data point when n is odd, or (n / 2)th data point + ((n / 2 + 1)th data point) / 2 when n is even – middle value of the dataset.
3. Mode = most frequently occurring value – value that appears most often in the dataset.
4. Range = Maximum value - Minimum value – difference between the largest and smallest values in the dataset.
5. Variance = Σ(xᵢ - Mean)² / (n - 1) – measure of spread or dispersion of the dataset.
6. Standard Deviation = √Variance – square root of the variance, representing the average distance of data points from the mean.
7. Skewness = (Σ(xᵢ - Mean)³ / (n - 1)) / (Standard Deviation)³ – measure of asymmetry of the dataset.
8. Kurtosis = (Σ(xᵢ - Mean)⁴ / (n - 1)) / (Standard Deviation)⁴ - 3 – measure of the "tailedness" or "peakedness" of the dataset.
9. ⚠️ p-value is NOT the probability that H₀ is true – it’s the probability of observing the data (or more extreme) if H₀ is true.
10. ⚠️ Correlation does not imply causation.