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.

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  • 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?

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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
A420610120806040
B315523754511569
C22531575504530
D5104404050160200
Total----310225380339
  • (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.

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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.

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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):

YearProd (Y)x (t-1963)xy
196040-39-120
196160-24-120
196250-11-50
196370000
1964551155
19657524150
19665039150
Total40002865

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.


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