(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.
(c) State some applications of index number.
(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)"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.
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 |
(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.
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).
(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)(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.
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
(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.
© 2026 Knowlet. All Rights Reserved.