Question 1

Positive correlation means:

Accepted Answer

Positive correlation implies both variables increase/decrease together.

Question 2

Paasche price index uses weights:

Accepted Answer

Paasche uses current-year quantities as weights.

Question 3

Cumulative frequency is:

Accepted Answer

Cumulative frequency sums frequencies up to a class.

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

Classification of data means:

Accepted Answer

Classification arranges data into groups based on common characteristics.

Question 6

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

Accepted Answer

c) Interquartile range (IQR)

Question 7

Least squares method fits a line by minimizing:

Accepted Answer

Least squares minimizes sum of squared residuals.

Question 8

Class interval (width) means:

Accepted Answer

Class interval is the difference between limits/boundaries of a class.

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

Primary data means data that is:

Accepted Answer

Primary data is collected directly for the specific study.

Question 17

Sampling error occurs because:

Accepted Answer

Sampling error arises from using a sample instead of whole population.

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

Correlation does not imply what?

Accepted Answer

Correlation does not imply causation (cause-and-effect).

Question 22

What is Paasche price index based on?

Accepted Answer

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

Question 23

Define mode.

Accepted Answer

Mode is the value (or class) which occurs with the highest frequency.

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

State one use of business statistics.

Accepted Answer

One use is forecasting sales/demand or decision making (any one).

Question 26

Write mean formula for discrete frequency series.

Accepted Answer

Mean (x̄) = Σfx / Σf.

Question 27

What is positive correlation?

Accepted Answer

Positive correlation means two variables move in the same direction (increase together or decrease together).

Question 28

What is a population?

Accepted Answer

Population is the entire group or universe of units under study.

Question 29

Define tabulation.

Accepted Answer

Tabulation is systematic presentation of classified data in a table with rows and columns.

Question 30

Define sampling.

Accepted Answer

Sampling is selecting a representative subset of the population to study and draw conclusions about the population.

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

Write any three types of correlation.

Accepted Answer

Types of correlation include:

1) Positive, negative and zero correlation (by direction).
2) Simple, multiple and partial correlation (by number of variables).
3) Linear and non-linear correlation (by form).

(Any three types can be written.)

Question 35

Differentiate mean, median and mode (any three points).

Accepted Answer

Mean, median and mode differ as follows:

| Point | Mean | Median | Mode |
|---|---|---|---|
| Basis | arithmetic average | middle value | most frequent value |
| Uses | further calculations | skewed/outlier data | typical/most common |
| Affected by extremes | yes | no | usually no |

(Any three points can be written.)

Question 36

Explain meaning and scope of business statistics with suitable examples.

Accepted Answer

Business statistics is the application of statistical methods to business problems. It helps convert raw data into useful information for planning, decision making, forecasting and control.

**Meaning:** Statistics (singular) is the science of collecting, organizing, presenting, analyzing and interpreting data. In business, it is used to study sales, costs, profits, customer preferences, production defects and market trends.

**Scope of business statistics** includes:

- collection of data (primary/secondary, sampling)
- classification, tabulation and presentation (tables/graphs)
- measures of central tendency and dispersion
- correlation and regression
- index numbers and time series
- basic probability and inference

For example, a company can use statistics to analyze monthly sales data, calculate average sales, measure variation, and forecast demand for the next quarter.

Thus, business statistics provides a scientific base for managerial decisions in uncertain situations.

Question 37

Explain common errors in frequency distribution and how to avoid them. Use a checklist table.

Accepted Answer

While preparing frequency distributions, students often make mistakes that reduce accuracy and interpretation.

Common errors and how to avoid them:

| Common error | Why it is wrong | How to avoid |
|---|---|---|
| Overlapping classes | creates confusion about where values belong | use non-overlapping intervals and boundaries |
| Unequal class widths (without reason) | distorts histogram and comparison | keep equal width unless justified |
| Missing observations in tallies | total frequency won’t match N | tally carefully and re-check |
| Wrong class limits/boundaries | causes gaps or double counting | convert inclusive to continuous boundaries |
| No total check | errors remain unnoticed | ensure Σf = N |

A simple final checklist is: decide appropriate classes, use correct limits/boundaries, tally correctly, and finally verify that total frequency equals number of observations.

Thus, careful construction and checking ensures correct frequency tables and reliable statistical results.

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