Section 6 - Chapter 1 - Introduction to Statistics Part I

Section 6 - Chapter 1 - Introduction to Statistics Part I - Presented by Rohan Sharma - The CMT Coach - Chartered Market Technician CMT Level 1 Study Material - CMT Level 1 Chapter Wise Short Notes - CMT Level 1 Course Content - CMT Level 1 2025 Exam Syllabus Visit Site : www.learn.ptaindia.com and www.ptaindia.com

1. Chapter 1 - Introduction to Statistics Part I Section 6 – Statistics Analysis Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

2. Agenda Introduction to Statistics Part 1 Descriptive Versus Inferential Statistics Measures of Central Tendency Measures of Dispersion This Content is Copyright Reserved Rights Copyright 2025@PTAIndia

3. Descriptive vs. Inferential Statistics Key Facts 1. Definition: o Descriptive Statistics: Summarizes and presents data meaningfully. o Inferential Statistics: Uses sample data to make predictions or generalizations about a larger population. 2. Primary Use: o Descriptive: Organizing, summarizing, and visualizing data. o Inferential: Drawing conclusions, hypothesis testing, and making predictions. 3. Techniques Used: o Descriptive: Measures of central tendency (mean, median, mode), measures of dispersion (variance, standard deviation), and visualizations (histograms, box plots). o Inferential: Confidence intervals, hypothesis tests (t-tests, chi-square tests), regression analysis, and probability distributions.

4. Descriptive vs. Inferential Statistics Key Facts 4. Sample vs. Population: o Descriptive: Works with the entire dataset (if available). o Inferential: Works with a sample to infer properties of a population. 5. Probability Involvement: o Descriptive: Does not involve probability; purely summarizes data. o Inferential: Uses probability theory to make predictions and conclusions.

5. Descriptive vs. Inferential Statistics Cheat Sheet . Feature Descriptive Statistics Inferential Statistics Purpose Summarizes and describes data Makes predictions or inferences about a population Data Type Raw data or entire dataset Sample data used to infer about population Key Metrics Mean, median, mode, standard deviation, range Hypothesis testing, confidence intervals, p-values Probability Use? No Yes Example Use Case Calculating the average age of students in a class Estimating the average age of all students in a country from a sample Graphical Tools Histograms, pie charts, box plots Regression plots, probability distributions

6. Descriptive vs. Inferential Statistics Comparison: Descriptive vs. Inferential Statistics . Comparison Aspect Descriptive Statistics Inferential Statistics Scope Only describes data Makes conclusions beyond the data Use of Samples Not required (uses entire dataset) Required (uses samples to infer about population) Mathematical Methods Basic calculations, charts, graphs Probability, statistical modeling, significance testing Certainty of Results Certain (as it describes the dataset) Uncertain (relies on probability and estimation) Application Example Finding the mean salary of employees in a company Predicting national salary trends from a small survey

7. Descriptive vs. Inferential Statistics Interpretation: When to Use Descriptive vs. Inferential Statistics? Descriptive Statistics: • Use when you want to summarize or visualize a dataset. • Example: Finding the average monthly sales of a company from past data. Inferential Statistics: • Use when you have a sample and want to make predictions or generalizations about a population. • Example: Conducting a survey of 1,000 voters to predict election results.

8. Descriptive vs. Inferential Statistics Interpretation: When to Use Descriptive vs. Inferential Statistics? Descriptive Statistics: • Use when you want to summarize or visualize a dataset. • Example: Finding the average monthly sales of a company from past data. Inferential Statistics: • Use when you have a sample and want to make predictions or generalizations about a population. • Example: Conducting a survey of 1,000 voters to predict election results.

9. Measures of Central Tendency – Key Fact 1 . Definition: Measures of central tendency summarize a dataset by identifying a single value that represents the middle or center of the data distribution. 2. Three Main Types: o Mean (Arithmetic Average) – Sum of all values divided by the number of values. o Median (Middle Value) – The middle number when data is arranged in order. o Mode (Most Frequent Value) – The most frequently occurring value(s) in the dataset. 3. Use Cases: o Mean: Best for normally distributed data. o Median: Best for skewed data or when there are outliers. o Mode: Best for categorical data or when identifying the most common value. 4. Sensitivity to Outliers: o Mean is highly affected by outliers. o Median is resistant to outliers. o Mode is not affected by outliers.

10. Measures of Central Tendency – Cheat Sheet Measure Formula Best For Sensitive to Outliers? Example Mean Mean= ∑Values/No. of Variables Normally distributed data Yes Average income of employees Median Middle value after sorting data Skewed data, data with outliers No Median home prices in a city Mode Most frequently occurring value(s) Categorical data, multimodal distributions No Most common exam grade in a class

11. Measures of Central Tendency Interpretation of Measures of Central Tendency 1. Mean Interpretation: o Represents the "typical" value when data is evenly distributed. o Example: If the average height of students is 170 cm, a randomly selected student is likely close to this value. 2. Median Interpretation: o More robust to outliers, representing the central position of ordered data. o Example: If the median income in a city is $50,000, half of the population earns below this amount and half earns above. 3. Mode Interpretation: o Helps identify the most frequent value, useful in categorical data. o Example: If most students score 85 on an exam, then 85 is the mode, showing the most common performance level.

12. Measures of Central Tendency Comparison of Mean, Median, and Mode Feature Mean Median Mode Definition Sum of values divided by count Middle value when sorted Most frequently occurring value Use Case Normally distributed data Skewed data, income, real estate prices Categorical or frequently occurring values Affected by Outliers? Yes, significantly No, robust No Applicability Continuous & numerical data Continuous & numerical data Categorical & numerical data Example Average test score Median house price Most popular shoe size

13. Measures of Dispersion Key Facts 1. Definition: Measures of dispersion describe the spread or variability of data in a dataset. 2. Key Types: o Range: Difference between the maximum and minimum values. o Variance: The average squared difference from the mean. o Standard Deviation (SD): Square root of variance; measures average deviation from the mean. o Interquartile Range (IQR): Difference between the 75th percentile (Q3) and 25th percentile (Q1). o Coefficient of Variation (CV): Standard deviation relative to the mean, expressed as a percentage .

14. Measures of Dispersion Key Facts 3 . Use Cases: o Range: Quick overview of spread but sensitive to outliers. o Variance & SD: Best for normally distributed data. o IQR: Best for skewed data, resistant to outliers. o CV: Useful for comparing variability across different datasets. 4. Impact of Outliers: o Variance & SD are highly affected. o IQR is resistant to outliers.

15. Measures of Dispersion Cheat Sheet Measure Best For Sensitive to Outliers? Example Range Quick spread estimation Yes Highest and lowest salaries in a company Variance (σ2\sigma^2σ2) Normally distributed data Yes Variability in stock prices Standard Deviation (σ\sigmaσ) Spread around mean Yes Risk (volatility) in finance Interquartile Range (IQR) Skewed data No Income distribution analysis Coefficient of Variation (CV) Comparing variability across datasets Yes Comparing price fluctuations of different stocks

16. Measures of Dispersion Comparison of Dispersion Measures Feature Range Variance Standard Deviation IQR CV Definition Max – Min Avg. squared deviations from the mean Square root of variance Q3 – Q1 SD relative to mean Best For Quick spread check Normally distributed data General spread measure Skewed data Comparing different datasets Affected by Outliers? Yes Yes Yes No Yes Comparison Across Datasets? No No No No Yes

17. Measures of Dispersion Interpretation of Measures of Dispersion 1. Range Interpretation: o Shows the simplest measure of spread but is unreliable due to sensitivity to outliers. o Example: If the lowest exam score is 50 and the highest is 98, the range is 48. 2. Standard Deviation Interpretation: o A low SD means data points are close to the mean. o A high SD means data is spread out. o Example: A stock with an SD of $2 is less volatile than one with an SD of $10 .

18. Measures of Dispersion Interpretation of Measures of Dispersion 3. Interquartile Range (IQR) Interpretation: o Shows the range of the middle 50% of the data, reducing the effect of extreme values. o Example: If Q1 = $40,000 and Q3 = $70,000, then IQR = $30,000, representing the central salary spread. o Allows com 4. Coefficient of Variation (CV) Interpretation: parisons across datasets with different units. o Example: If stock A has a CV of 15% and stock B has a CV of 25%, stock B is more volatile

19. Measures of Dispersion Key Takeaways ✅ Standard deviation is the most common measure of dispersion but is affected by outliers. ✅ IQR is useful for skewed data since it ignores extreme values. ✅ CV is best when comparing variability across different datasets. ✅ Higher dispersion means more variability in data, which can indicate higher risk in finance or more diversity in research.

20. Next Chapter 2 - Introduction to Statistics Part II Section 6 – Statistics Analysis Presented By : This Content is Copyright Reserved Rights Copyright 2025@PTAIndia