Section 6 - Chapter 1 - Introduction to Statistics Part I

Chapter 1 - Introduction to Statistics Part I
Section 6 – Statistics Analysis
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Agenda
 Introduction to Statistics Part 1
 Descriptive Versus Inferential Statistics
 Measures of Central Tendency
 Measures of Dispersion

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.

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.

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

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

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.

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.

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

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.

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

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.

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.

Cheat Sheet
Measure Best For
Sensitive to
Outliers?
Example
Range Quick spread estimation Yes
Highest and lowest
salaries in a company
Variance (σ2sigma^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

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

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.

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 com4. 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

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.

Next Chapter 2 - Introduction to Statistics Part II
Section 6 – Statistics Analysis
Presented By :

Section 6 - Chapter 1 - Introduction to Statistics Part I

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Section 6 - Chapter 1 - Introduction to Statistics Part I