Question 1

Dispersion refers to:

Accepted Answer

Dispersion measures how far data values scatter around the average.

Question 2

Paasche price index uses weights:

Accepted Answer

Paasche uses current-year quantities as weights.

Question 3

Lower CV indicates:

Accepted Answer

Lower CV means lower relative variation and more consistency.

Question 4

What is the primary purpose of a box plot (box-and-whisker plot)?

Accepted Answer

c) To visualize the distribution of data and identify outliers

Question 5

In a continuous series, median depends on:

Accepted Answer

Median class is located using N/2 and cumulative frequency.

Question 6

Which measure of dispersion is less affected by outliers compared to the range?

Accepted Answer

c) Interquartile range (IQR)

Question 7

A ratio scale has:

Accepted Answer

Ratio scale has equal intervals and a true zero (income, weight).

Question 8

Coefficient of variation (CV) is:

Accepted Answer

CV = (SD/Mean) × 100.

Question 9

What is the formula for calculating the standard deviation of a dataset?

Accepted Answer

a) Square root of the variance

Question 10

The interquartile range (IQR) represents the range between the:

Accepted Answer

b) First quartile (Q1) and third quartile (Q3)

Question 11

Cyclical variations usually last:

Accepted Answer

Cyclical variations are multi-year business cycle movements.

Question 12

What does the term p-value represent in hypothesis testing?

Accepted Answer

a) The probability of making a Type I error

Question 13

Seasonal variations are:

Accepted Answer

Seasonal variations repeat within a year.

Question 14

Irregular variations are:

Accepted Answer

Irregular component is unpredictable shocks.

Question 15

Which of the following is a measure of dispersion?

Accepted Answer

c) Range

Question 16

Cumulative frequency is:

Accepted Answer

Cumulative frequency sums frequencies up to a class.

Question 17

Mean is most affected by:

Accepted Answer

Mean uses all values and is influenced by extreme values.

Question 18

In Y = a + bX, b represents:

Accepted Answer

b is slope: change in Y per unit change in X.

Question 19

What does the term correlation measure in statistics?

Accepted Answer

b) Relationship between two variables

Question 20

In normal distribution:

Accepted Answer

For normal, mean=median=mode.

Question 21

What is sampling error?

Accepted Answer

Sampling error is the difference between a sample result and the true population value due to studying only a sample.

Question 22

What is Paasche price index based on?

Accepted Answer

Paasche price index uses current year quantities (q1) as weights.

Question 23

What is negative correlation?

Accepted Answer

Negative correlation means two variables move in opposite directions (one increases while the other decreases).

Question 24

What is a base year?

Accepted Answer

Base year is the reference period against which changes are compared (index in base year is taken as 100).

Question 25

What is cumulative frequency?

Accepted Answer

Cumulative frequency is the running total of frequencies up to a given class (less-than) or from a class (more-than).

Question 26

What is a scatter diagram?

Accepted Answer

A scatter diagram is a graph of paired values (x, y) used to visually study correlation.

Question 27

Define secondary data.

Accepted Answer

Secondary data are data already collected by others and used for the current study.

Question 28

Define frequency distribution.

Accepted Answer

Frequency distribution is a table showing frequencies of observations for different values or class intervals.

Question 29

Define range.

Accepted Answer

Range is the difference between the largest and the smallest value in the data set (R = L − S).

Question 30

Write mean formula for individual series.

Accepted Answer

Mean (x̄) = Σx / n.

Question 31

Write any three precautions/limitations of regression.

Accepted Answer

Precautions/limitations include:

1) Do not assume causation; regression shows association/prediction.
2) Avoid extrapolation beyond observed data range.
3) Outliers and unstable relationships can distort the regression line.

(Any three points can be written.)

Question 32

Differentiate between Laspeyres and Paasche index (any three points).

Accepted Answer

Difference:

| Point | Laspeyres | Paasche |
|---|---|---|
| Weights | base quantities (q0) | current quantities (q1) |
| Tendency | may overstate inflation | may understate inflation |
| Data need | easier (base q) | harder (current q) |

(Any three points can be written.)

Question 33

Differentiate between seasonal and cyclical variations (any three points).

Accepted Answer

Seasonal vs cyclical differences:

| Point | Seasonal | Cyclical |
|---|---|---|
| Time period | within one year | more than one year |
| Cause | seasons, festivals | business cycles |
| Example | festival sales peak | recession reduces demand |

(Any three points can be written.)

Question 34

Differentiate between primary data and secondary data (any three points).

Accepted Answer

Primary and secondary data differ as follows:

| Point | Primary data | Secondary data |
|---|---|---|
| Source | collected first-hand | collected earlier by others |
| Cost/time | higher | lower |
| Suitability | specific to objective | may not fit perfectly |

(Any three points can be written.)

Question 35

Write any three merits and demerits of range.

Accepted Answer

Range merits/demerits:

Merits:
1) Very simple and quick to compute.
2) Useful for rough comparison.

Demerits:
3) Depends only on extreme values and ignores the rest.

(Any three points can be written.)

Question 36

Explain primary and secondary data, with advantages and limitations of each.

Accepted Answer

Data can be collected from two main sources: primary and secondary.

**Primary data** are collected first-hand by the investigator for the specific purpose of the study (through survey, interview, observation, questionnaire, etc.). **Secondary data** are already collected by someone else and are available in published or unpublished form (government reports, company records, journals, websites).

| Point | Primary data | Secondary data |
|---|---|---|
| Advantage | specific to objective; more control | cheaper; quick availability |
| Limitation | costly and time-consuming | may be outdated or not suitable |

Primary data is more suitable when accurate and specific information is required. Secondary data is useful for background study, trend analysis and preliminary research.

Thus, the choice depends on time, cost, purpose and availability of reliable data.

Question 37

Write a detailed note on selecting an appropriate measure of central tendency. Use a comparison table.

Accepted Answer

No single average is best in all cases. The choice of mean, median or mode depends on the nature of data and the purpose of analysis.

| Situation | Best measure | Reason |
|---|---|---|
| Data is symmetric and no extreme values | Mean | uses all values and supports further calculations |
| Data is skewed or has outliers (income, wages) | Median | not affected by extreme values |
| Need the most common value (popular size/brand) | Mode | shows most frequent/typical value |
| Qualitative/categorical emphasis | Mode | identifies most common category |

For example, average income using mean can be misleading if a few people have very high incomes. In such cases, median provides a better “typical” income. Similarly, a retailer chooses mode to know the most demanded size.

Therefore, selecting the correct measure of central tendency improves accuracy, interpretation and decision making in business.

Question 38

Explain Fisher’s ideal index and why it is called ideal. Include tests in your answer.

Accepted Answer

Fisher’s ideal index is a weighted index number that combines the advantages of Laspeyres and Paasche indices. It is defined as the geometric mean of Laspeyres (PL) and Paasche (PP) indices:

PF = √(PL × PP)

Why it is called “ideal”:

1) It uses both base year and current year quantities indirectly, reducing bias.
2) It satisfies important tests of adequacy:

- **Time reversal test:** P01 × P10 = 1
- **Factor reversal test:** P01 × Q01 = V01

Laspeyres uses base weights and may overstate price rise; Paasche uses current weights and may understate. Fisher balances both by taking geometric mean.

Therefore, Fisher’s index is called ideal because it is more reliable and satisfies the key tests, making it suitable for accurate index number construction.

Question 39

Explain conditional probability and Bayes’ theorem. Write the formulas and one business use.

Accepted Answer

Conditional probability means the probability of event A happening when it is known that event B has already occurred. It is written as P(A|B) and is defined by:

P(A|B) = P(A ∩ B) / P(B), where P(B) > 0.

Bayes’ theorem is used to revise (update) probabilities when new information is obtained. It connects P(A|B) with P(B|A) and the prior probability P(A):

P(A|B) = [P(B|A) P(A)] / P(B).

**Business use:** In quality control, Bayes’ theorem helps find the probability that a product is actually defective given that a test reports “defective”, especially when the test is not perfectly accurate.

Thus, conditional probability and Bayes’ theorem are essential tools for decision-making under uncertainty.

Question 40

Explain simple linear regression and interpret the regression equation with a worked example.

Accepted Answer

Simple linear regression studies the relationship between two variables and provides a prediction equation. When Y depends on X, the regression equation is written as:

Y = a + bX

where a is the intercept and b is the slope (regression coefficient). The slope tells how much Y is expected to change when X increases by one unit.

**Worked example:**
Suppose the regression equation is:

Y = 20 + 3X

If X = 10, then predicted Y = 20 + 3(10) = 50.

Interpretation:
- Intercept 20: the base value of Y when X is zero.
- Slope 3: for each 1 unit rise in X, Y increases by 3 units.

Thus, regression is very useful for business forecasting, such as predicting sales (Y) from advertising (X).

Business Statistics — Question Paper

20 more questions to unlock