Descriptive Statistics

What is Descriptive Statistics? #

Descriptive statistics is used to summarize and describe the main features of a dataset.

It answers:

• What is the average?
• How spread out is the data?
• Are there unusual values?

Sample Dataset #

Let’s use this data:

10, 20, 30, 40, 50

Mean (Average) #

Definition #

The mean is the average of all values.

Formula #

$$\text{Mean} = \frac{\text{Sum of all values}}{\text{Number of values}}$$Mean=Number of valuesSum of all values​

Example #

$$(10 + 20 + 30 + 40 + 50) / 5 = 30$$(10+20+30+40+50)/5=30

Mean = 30

Use #

• General average of data

Median #

Definition #

The middle value when data is sorted

Example #

10, 20, 30, 40, 50

Middle value = 30

Even Dataset Example #

10, 20, 30, 40

Median = (20 + 30) / 2 = 25

Use #

• Better when data has outliers

Mode #

Definition #

The value that appears most frequently

Example #

10, 20, 20, 30, 40

Mode = 20

Use #

• Useful for categorical data

Range #

Definition #

Difference between maximum and minimum values

Formula #

$$\text{Range} = \text{Max} – \text{Min}$$Range=Max−Min

Example #

$$50 – 10 = 40$$50−10=40

Range = 40

Use #

• Shows spread of data

Variance #

Definition #

Measures how far values are from the mean

Formula (Conceptual) #

$$\text{Variance} = \frac{\sum (x – \text{mean})^2}{n}$$Variance=n∑(x−mean)2​

Meaning #

• High variance → data spread out
• Low variance → data close to mean

Standard Deviation #

Definition #

Square root of variance

Formula #

$$\text{Std Dev} = \sqrt{\text{Variance}}$$Std Dev=Variance​

Meaning #

• Low → data is consistent
• High → data is spread out

Example Insight #

• Std Dev = 2 → tightly grouped
• Std Dev = 20 → widely spread

Quartiles #

Definition #

Divide data into 4 equal parts

Types #

Example #

10, 20, 30, 40, 50

• Q1 = 20
• Q2 = 30
• Q3 = 40

Interquartile Range (IQR) #

Formula #

$$IQR = Q3 – Q1$$IQR=Q3−Q1

Example #

$$40 – 20 = 20$$40−20=20

IQR = 20

Outliers #

Definition #

Values that are very far from the rest of the data

Detection (Using IQR) #

Lower limit:$$Q1 – 1.5 \times IQR$$Q1−1.5×IQR

Upper limit:$$Q3 + 1.5 \times IQR$$Q3+1.5×IQR

Example #

If:

• Q1 = 20
• Q3 = 40
• IQR = 20

Lower = 20 – 30 = -10
Upper = 40 + 30 = 70

Any value outside this range = outlier

Example Data #

10, 20, 30, 40, 100

100 is an outlier

Summary Table #

When to Use What #

• Use Mean → normal data
• Use Median → skewed data
• Use Std Dev → variability
• Use IQR → outlier detection