UNIT – 3

1. Define Range

Range is the simplest measure of dispersion. It is the difference between the largest and smallest value in a data set and depends only on extreme items.

Formula:

R = L - S

2. Range Based Problem

Given data: 27, 30, 35, 36, 38, 40, 43

L = 43
S = 27

Range = 43 − 27 = 16

Coefficient of Range = (L-S) / (L+S) = 16 / 70 = 0.228

3. Merits and Demerits of Range

Merits:

  • Simplest method of dispersion.
  • Easy to calculate and understand.

Demerits:

  • Depends only on extreme values.
  • Ignores all other observations.

4. Define Quartile Range

Quartile Range (Inter-Quartile Range) is the difference between upper quartile (Q₃) and lower quartile (Q₁).

IQR = Q₃ - Q₁

5. Semi-Inter Quartile Range (Quartile Deviation)

It is half of the Inter-Quartile Range.

Q.D = (Q₃ - Q₁) / 2

6. Formula for Mean Deviation

Mean Deviation about Mean:

MDₓ̄ = Σ |X - X̄| / N

Mean Deviation about Median:

MDₘ = Σ |X - M| / N

7. Define Skewness

Skewness is the lack of symmetry in a distribution. If the curve shifts left or right, the data is skewed.

8. Characteristics of Dispersion and Skewness

Dispersion:
Measures how data values spread from the average.

Skewness:
Shows the degree of asymmetry in the distribution.

9. Difference Between Merits and Demerits of Skewness

Merits Demerits
Identifies direction and degree of asymmetry Sensitive to extreme values
Reveals information averages cannot show Different methods may give different results

10. Define Dispersion

Dispersion measures the variation of items in a data set. It shows how values spread from the central average.

Methods:

  • Range
  • Quartile Deviation
  • Mean Deviation
  • Standard Deviation
UNIT – 4

1. Define Curve Relation or Correlation

Correlation refers to the degree of relationship between two or more variables. If change in one variable affects another, they are correlated.

If the change does not follow a constant ratio, it is called curvi-linear (non-linear) correlation.

2. Uses of Curve Relation (Correlation)

  • Used in physical and social sciences.
  • Helps economists study price–quantity relationships.
  • Helps businessmen estimate cost and sales.
  • Measures relationship between income and expenditure.
  • Basis for regression analysis.

3. Types of Correlation

Correlation is classified into four categories:

  1. Positive and Negative
  2. Linear and Non-linear
  3. Partial and Total
  4. Simple and Multiple

These classifications show direction and complexity of relationships.

4. Definitions of Correlation Types

Positive and Negative

Positive: Variables move in same direction.

Negative: Variables move in opposite direction.

Linear and Non-linear

Linear: Constant ratio of change (straight line).

Non-linear: No constant ratio (curve line).

Partial and Total

Partial: Studies two variables excluding others.

Total: Considers all relevant variables together.

Simple and Multiple

Simple: Involves only two variables.

Multiple: Involves more than two variables.

5. Write Two Regression Equations

1. Regression Equation of Y on X:

Y - Ȳ = bYX(X - X̄)

2. Regression Equation of X on Y:

X - X̄ = bXY(Y - Ȳ)

6. Regression Coefficients Formulas

bYX = Σ(X - X̄)(Y - Ȳ) / Σ(X - X̄)2

or

bYX = r (σy / σx)


bXY = Σ(X - X̄)(Y - Ȳ) / Σ(Y - Ȳ)2

or

bXY = r (σx / σy)

7. Difference Between Correlation and Regression

Correlation Regression
Measures degree and direction of relationship Provides functional relationship for prediction
Describes linear association only Used for prediction and estimation
Does not establish cause-effect Shows dependent and independent variables