FYUG Even Semester Exam, 2025 STATISTICS (2nd Semester) Index Number and Time Series Analysis (STAIDC-151)

Time: 3 Hours | Full Marks: 70 | Pass Marks: 28

UNIT-I

Question 1 (Any 4) [1x4=4]

(a) Define index number.

An index number is a specialized average designed to measure the changes in a group of related variables over a period of time.

(b) State some limitations of index number.

They are often based on samples and may not represent the entire population.

Errors in the collection of data or choice of base year can lead to misleading results.

(c) State some applications of index number.

[span_8](start_span)

Used as economic barometers to measure the "pulse" of an economy.[span_8](end_span)

Measuring changes in the cost of living and purchasing power.

(d) Write Paasche's index number formula.

P01 = [Sum(p1 * q1) / Sum(p0 * q1)] * 100

(e) What is base year in an index number?

[span_14](start_span)

The base year is a reference year or standard period against which changes in the current period are compared.[span_14](end_span)

Question 2(a) [2]

"Index numbers are economic barometers." Explain.

Index numbers are called economic barometers because they measure the state of the economy just as a barometer measures atmospheric pressure. They reflect shifts in business activity, inflation, and production, allowing policymakers to understand economic trends and health.

Question 3(b) [8]

Construct price index numbers for 1995 with 1990 as base:

Comm.	p0	q0	p1	q1	p1q0	p0q0	p1q1	p0q1
A	4	20	6	10	120	80	60	40
B	3	15	5	23	75	45	115	69
C	2	25	3	15	75	50	45	30
D	5	10	4	40	40	50	160	200
Total	-	-	-	-	310	225	380	339

(i) Laspeyres': (Sum p1q0 / Sum p0q0) * 100 = (310/225) * 100 = 137.78

(ii) Paasche's: (Sum p1q1 / Sum p0q1) * 100 = (380/339) * 100 = 112.09

(iii) Marshal-Edgeworth: [Sum(p1q0+p1q1)/Sum(p0q0+p0q1)] * 100 = (690/564) * 100 = 122.34

(iv) Fisher's: Sqrt(L * P) = Sqrt(137.78 * 112.09) = 124.27

UNIT-II

Question 4 (Any 4) [1x4=4]

(a) Define time reversal test.

[span_24](start_span)

A test requiring that if the time subscripts (0 and 1) are interchanged, the resulting index should be the reciprocal of the original: P01 * P10 = 1.[span_24](end_span)

(c) Fill in the blank: Fisher's index number is known as ideal index number.

(d) Fill in the blank: Fisher's index number is Geometric Mean of Laspeyres' and Paasche's index number.

Question 6(a) [2+4+2=8]

Define CPI, Steps, and Uses.

Definition: Consumer Price Index (CPI) measures the average change over time in the prices paid by consumers for a representative basket of goods and services.

Steps: 1. Selection of the consumer group. 2. Conduct family budget inquiry. 3. Selection of base year. 4. Selection of items/commodities. 5. Collection of price quotations.

Uses: Used to calculate Real Wages, deflation of income, and adjustment of dearness allowance (DA).

UNIT-III

Question 7 (Any 4) [1x4=4]

(a) Define time series.

A set of observations recorded at successive intervals of time.

(d) Define trend in time series.

[span_35](start_span)

Trend is the long-term smooth general tendency of the data to increase or decrease over a long period.[span_35](end_span)

Question 8(b) [8]

(i) Fire in a factory: Irregular/Random variation.

(ii) Sale of umbrella during summer: Seasonal variation.

(iii) Fall in death rate due to science: Secular Trend.

(iv) Flood due to heavy rain: Irregular/Random variation.

UNIT-IV

Question 12(a) [8]

Fit a straight-line equation (Y = a + bX):

Year	Prod (Y)	x (t-1963)	x²	xy
1960	40	-3	9	-120
1961	60	-2	4	-120
1962	50	-1	1	-50
1963	70	0	0	0
1964	55	1	1	55
1965	75	2	4	150
1966	50	3	9	150
Total	400	0	28	65

a = Sum(Y)/n = 400/7 = 57.14
b = Sum(xy)/Sum(x²) = 65/28 = 2.32
Equation: Y = 57.14 + 2.32X

UNIT-V

Question 13 (Any 4) [1x4=4]

(a) Define seasonality.

Regular periodic fluctuations that repeat within a period of 12 months (e.g., weather, festivals).

(d) Blank: Moving average method eliminates short-term/seasonal variations.

Exam Focus Enhancements

Important Formulas List

Fisher's Index: P01 = Sqrt([Sum p1q0/Sum p0q0] * [Sum p1q1/Sum p0q1]) * 100

Straight Line Trend: Y = a + bX; where a = Sum(Y)/n and b = Sum(XY)/Sum(X²)

[span_50](start_span)

Time Reversal Test: P01 * P10 = 1[span_50](end_span)

Answer Presentation Strategy

For Unit I & II numericals, always show the calculation table clearly with columns for p1q0, p0q0, etc.

In Time Series, clearly state the value of 'n' and the origin of 'x' when fitting a trend.

[span_54](start_span)

Define components of time series with real-world examples to justify the classification.[span_54](end_span)