Business Statistics and Research Methods MCQ Questions and Solutions with Explanations | Commerce

Understanding Scales of Measurement:
In statistics, we use different scales to measure data. Think of it like measuring things with different rulers.

Nominal Scale: This is like labeling things with names. We just give them categories without any order or ranking.
Example: Colors (red, blue, green), Gender (male, female), Types of cars (sedan, SUV, truck).

Ordinal Scale: This scale has order or ranking, but the difference between each rank isn't necessarily equal.
Example: Education level (high school, bachelor's, master's), Customer satisfaction (very satisfied, satisfied, neutral, dissatisfied, very dissatisfied).

Interval Scale: Here, the difference between each point is equal, but there's no true zero point.
Example: Temperature in Celsius or Fahrenheit (0°C doesn't mean there's no temperature).

Ratio Scale: This scale has equal intervals and a true zero point. Zero means the absence of the thing being measured.
Example: Height, weight, age, income.

Applying it to the Question:
The question asks about classifying respondents by gender (male, female). We're just assigning labels, not ranking or measuring anything numerically. Therefore, this is a nominal scale.

Therefore, the correct answer is B: Nominal scale

Laspeyre's index and Paasche's index are two important methods used to calculate price indices in economics. Laspeyre's index is based on the geometric mean of these two indices.

Laspeyre's Index: It is a price index where the base-year quantities are used as weights. Mathematically, it is represented as:

Laspeyre's Index = (Σ Current Year Prices * Base Year Quantities) / (Σ Base Year Prices * Base Year Quantities)

Paasche's Index: It is another price index where the current-year quantities are used as weights. Mathematically, it is represented as:

Paasche's Index = (Σ Current Year Prices * Current Year Quantities) / (Σ Base Year Prices * Current Year Quantities)

The geometric mean of Laspeyre's and Paasche's indices is used to reduce the bias that can be present in each of these indices when used alone. It provides a more balanced measure of price change.

So, the correct answer is Option C: Geometric mean of Laspeyre's and Paasche's index.