Branch of statistics concerned with summarizing, organizing and describing a Dataset.
It answers questions like:
- What is typical?
- How spread out is the data?
- Are there extreme values?
- How is the data distributed?
- Are there patterns or irregularities?
Importantly, descriptive statistics do not attempt to make predictions or draw conclusions about a larger population. They simple describe the data you have.
For example:
“The average daily sales were 1,500 and $3,000.”
This is descriptive statistics.
Main Categories
- Measures of Central Tendency
- Measures of Dispersion (Variability)
- Measures of Position
- Measures of Shape
- Measures of Frequency and Distribution
Measures of Central Tendency
These describe the center or “typical” value of the data.
Mean
The arithmetic average of all observations.
Usefulness
Provides a single value representing the dataset.
Use Cases
- Average sales
- Average salary
- Average response time
- Average test score
Limitations
Highly sensitive to outliers: 100, 150, 10000 → Mean = 3,416.67 → Not representative
Median
The middle value after sorting the data.
Usefulness
Represents the “typical” value when data contains outliers.
Use Cases
- Income distributions
- Housing prices
- Daily sales with occasional spikes
Advantages
Very robust against extreme values.
Mode
The most frequently occurring value.
Usefulness
Identifies the most common observation
Use Cases
- Most purchased product
- Most common shoe size
- Most common customer segment
- Most frequent error code
Limitations
May have:
- No mode
- One mode
- Multiple modes
Measures of Dispersion: Variability
These tell you how spread out the data is. Two datasets may have the same mean but completely different variability.
Range
Difference between maximum and minimum. → 1, 3, 8, 10 → Range = 9
Usefulness
Quick estimate of spread
Use Cases
- Temperature variation
- Price ranges
- Delivery times
Limitations
Depends only on two observations.
Variance
See Variance.
Usefulness
Fundamental measure of variability.
Use Cases
- Risk analysis
- Quality control
- Machine learning
- Statistical modeling
Limitations
Units become squared. This makes interpretation difficult.
Standard Deviation
Intuition
Represents the typical distance from the mean. Example:
- Average sales: → $2,000
- Standard deviation: → $500
- Interpretation: → Most observations tend to lie around ±$500 from the average.
Usefulness
The most important measure of variability.
Use Cases
- Sales volatility
- Stock risk
- Manufacturing consistency
- Academic performance
Interquartile Range: IQR
Difference between: Contains the middle 50% of observations.
Usefulness
Measures spread while ignoring outliers.
Use Cases
- Income analysis
- Sales analysis
- Outlier detection
Measures of Position
These indicate where an observation lies relative to others.
Minimum
Smallest observation.
Maximum
Largest observation.
Quartiles
Divide data into four equal parts.
- Q1 = 25th percentile
- Q2 = Median
- Q3 = 75th percentile
Usefulness
Describe how values are distributed.
Use Cases
- Salary analysis
- Exam scores
- Customer spending
Percentiles
Divide data into 100 parts.
→ 90 th percentile: >> A value larger than 90% of observations.