Descriptive Analytics
Name: Meet Prajapati
Enrollment No:12202130501040
Branch : Computer Science and Design
Batch: 1C13
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Introduction to Descriptive
Analytics
What is it?
Why It Matters
Definition: Analysis of historical
It forms the foundation for all
data to understand "what
data analysis, enabling data-
happened." It's about
driven decisions and identifying
summarizing and describing the
crucial patterns and trends for
main features of datasets.
business reporting.
Key Applications
•
Sales performance
•
Customer behavior
•
Quality control
•
Market research
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Unpacking Data Types
Quantitative Data (Numerical)
Qualitative Data (Categorical)
•
Discrete: Countable values (e.g., number of customers: 10, 11, 12)
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Nominal: No inherent order (e.g., blood type: A, B, AB, O)
•
Continuous: Measurable within ranges (e.g., height: 5.6 ft, 5.65 ft)
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Ordinal: Meaningful order (e.g., satisfaction: Poor < Fair < Good <
Excellent)
Understanding these classifications is crucial as it dictates the
appropriate statistical methods and visualization choices, influencing
overall analysis techniques.
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Measurement Scales
1
Nominal Scale
Categories only, no order (e.g., Gender). Only mode is applicable for statistics.
2
Ordinal Scale
Ranked categories (e.g., Education levels). Mode and median are applicable.
3
Interval Scale
Equal intervals, no true zero (e.g., Temperature °C). Mode, median, and mean apply.
4
Ratio Scale
Equal intervals with true zero (e.g., Height). All statistical measures are applicable.
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Population vs. Sample
Population
Sample
Definition: The complete set of all elements under study
Definition: A subset selected from the population (e.g., 200
(e.g., All students in a university). Represented by N (size), μ
randomly selected students). Represented by n (size), x̄
(mean), σ (standard deviation).
(mean), s (standard deviation).
Key Differences: Samples are more economical and allow for faster analysis. While studying entire populations is often
infeasible, a good sample can represent the population well.
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Measures of Central Tendency
Mean (Average)
The sum of all values divided by the number of values. Best for
symmetric distributions and interval/ratio data. Example: Scores
80, 85, 90 → Mean = 85
Median (Middle Value)
The 50th percentile when data is ordered. Ideal for skewed
distributions and ordinal data. Example: 12, 15, 18, 20, 25 →
Median = 18
Mode (Most Frequent)
The value appearing most often in a dataset. Best for categorical
data and identifying typical categories. Example: 2, 3, 4, 4, 5 →
Mode = 4
Percentiles, Deciles, and Quartiles
Percentiles (P)
Deciles (D)
Quartiles (Q)
Divide data into 100 equal parts. P₇₅
Divide data into 10 equal parts. D₅
Q₁ (25th percentile), Q₂ (50th
means 75% of values are below this
(50th percentile) is the Median, useful
percentile/Median), Q₃ (75th
point, useful for comparing individual
for understanding distribution
percentile). The IQR = Q₃ - Q₁ is the
performance.
spread.
Interquartile Range.
Example: Test Scores (60, 70, 75, 80, 85, 90, 95)
For this dataset:
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Q₁ (25th percentile) = 70
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Q₂ (50th percentile) = 80
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Q₃ (75th percentile) = 90
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IQR = 90 - 70 = 20
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Measures of Variation: Range and IQR
Range
Interquartile Range (IQR)
Formula: Maximum - Minimum. While simple to calculate, it's highly sensitive
Formula: Q₃ - Q₁. This measures the spread of the middle 50% of data,
making it less affected by extreme outliers. Often used in box plots and for
to outliers.
•
Example: Data: 12, 15, 18, 25, 30 → Range = 30 - 12 = 18
outlier detection.
Why Variation Matters: Two datasets can have the same mean but vastly different reliabilities. Understanding variation helps assess data consistency.
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Variance and Standard Deviation
Variance (σ² or s²)
Standard Deviation (σ or s)
The average of the squared deviations from the mean. It
The square root of the variance. Its advantage is being in the
quantifies the spread of data points around the mean.
same units as the original data, providing a more intuitive
Population: σ² = Σ(x - μ)²/N
understanding of average deviation from the mean.
Sample: s² = Σ(x - x̄)²/(n-1)
Example Calculation: Data: 2, 4, 6, 8, 10
•
Mean = 6
•
Deviations: -4, -2, 0, 2, 4
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Squared deviations: 16, 4, 0, 4, 16
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Variance = 40/5 = 8
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Standard Deviation = √8 ≈ 2.83
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Coefficient of Variation and Measures of Shape
Coefficient of Variation (CV)
Measures of Shape
Formula: CV = (σ/μ) × 100%
Skewness: Describes the asymmetry of the probability distribution.
Purpose: Compares variability across different datasets, even with different units or
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Symmetric: Mean = Median = Mode
scales. A lower CV indicates greater consistency.
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Right Skewed: Mean > Median > Mode
Example: Dataset A (mean=50, SD=5) vs Dataset B (mean=500, SD=25). CV_A = 10%,
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Left Skewed: Mode > Median > Mean
CV_B = 5% → Dataset B is more consistent.
Kurtosis: Describes the "tailedness" of the distribution.
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Mesokurtic: Normal bell curve
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Leptokurtic: Peaked distribution
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Platykurtic: Flat distribution
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