TGPSC MPSO / ASO · Paper II · Topic 6
TGPSC MPSO / ASO Time Series & Index Numbers questions with answers
21 questions from TGPSC ASO Paper II Mock 1 with answers and TGPSC ASO Paper II Challenge 1 with answers. Try each one, then tap Show answer.
6.1Time series: components, trend & seasonal variationNotesPractise this chapter · Set 1 free
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The quarterly trend of a firm's sales is Yc = 50 + 2X, with origin at the first quarter of 2024 and X in quarters. Under the additive model the seasonal effect of the fourth quarter is −5. The forecast for the fourth quarter of 2025 is
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Answer B. 59
From Q1 2024 (X = 0) to Q4 2025 is 7 quarters, so trend = 50 + 2 × 7 = 64. Adding the seasonal effect: 64 − 5 = 59.
Source: Standard method (degree-level analysis of time series)
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The values of a series for 2016 to 2021 are 30, 34, 38, 36, 40 and 44. Using a 4-yearly centred moving average, the trend value for 2018 is
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Answer B. 35.75
4-yearly averages: 138/4 = 34.5 (between 2017 and 2018) and 148/4 = 37 (between 2018 and 2019). Centring: (34.5 + 37)/2 = 35.75 for 2018.
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Under the multiplicative model, the trend value of a quarter is 200 units, the seasonal index is 110, the cyclical relative is 95 and the irregular relative is 100. The original value of the series is
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Answer C. 209
Y = T × S × C × I = 200 × 1.10 × 0.95 × 1.00 = 209.
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Consider the following statements about the link relative method:
1. The link relative of the first season cannot be computed for the first year of the data.
2. Link relatives are obtained by dividing each figure by its centred moving average.
Which of the statements given above is/are correct?
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Answer A. 1 only
A link relative needs the previous season's figure, so the first season of the first year has none. Dividing by the moving average is the ratio-to-moving-average method.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Consider the following statements:
1. The additive model Y = T + S + C + I assumes that the four components are independent of one another.
2. In the multiplicative model Y = T × S × C × I, the trend is in original units while S, C and I are expressed as relatives (ratios or indices).
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
The additive model treats components as independent and all in original units. The multiplicative model treats them as interdependent: T is in original units and S, C, I are ratios/percentages of the trend.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
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Match List I (trend) with List II (property of the trend values):
List I:
A. Straight-line trend
B. Second-degree parabola
C. Exponential trend
D. Moving average trend
List II:
1. Second differences are constant
2. No mathematical equation is obtained
3. First differences are constant
4. The ratio of successive values is constant
Choose the correct answer.
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Answer D. A-3, B-1, C-4, D-2
A straight line rises by a constant amount (constant first differences). A parabola has constant second differences. An exponential curve rises at a constant rate (constant ratio). A moving average gives values but no equation.
Source: Standard definition (degree-level analysis of time series, as in Telangana B.A./B.Com statistics texts)
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Match List I (example) with List II (component of time series):
List I:
A. Steady rise in India's population over decades
B. Higher sale of umbrellas every monsoon
C. Alternating boom and slump in business every few years
D. Fall in factory output due to a sudden strike
List II:
1. Irregular variation
2. Cyclical variation
3. Seasonal variation
4. Secular trend
Select the correct answer using the code given below.
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Answer D. A-4, B-3, C-2, D-1
Long-term population growth is secular trend; monsoon umbrella sales are seasonal; boom-slump over years is cyclical; a sudden strike causes irregular variation.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
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Consider the following statements:
1. Seasonal variations have a fixed period, so they can be predicted fairly accurately.
2. Cyclical variations have a fixed period of 12 months.
Which of the statements given above is/are correct?
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Answer A. 1 only
Seasonal variations repeat regularly within a year and are predictable. Cyclical variations last more than a year and vary in length, so statement 2 is false.
Source: Standard definition (degree-level analysis of time series, as in Telangana B.A./B.Com statistics texts)
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Which of the following is NOT generally regarded as a use of time series analysis?
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Answer B. Measuring the degree of association between two different variables at one point of time
Time series analysis studies one variable over time: its past behaviour, forecasting and evaluation of performance. Association between two variables at a point of time is the subject of correlation.
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
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A series for seven years reads 12, 15, 18, 14, 20, 22, 19. Match List I with List II.
List I:
- A. 3-yearly moving average for year 2
- B. 3-yearly moving average for year 3
- C. First 4-yearly moving average before centring
- D. 4-yearly centred moving average for year 3
List II:
- 1. 15.75
- 2. 15
- 3. 14.75
- 4. 15.67
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Answer A. A-2, B-4, C-3, D-1
The correct match is A-2, B-4, C-3, D-1. The 3-yearly averages are (12 + 15 + 18)/3 = 15 for year 2 and (15 + 18 + 14)/3 = 15.67 for year 3. The first two 4-yearly averages are 59/4 = 14.75 and 67/4 = 16.75; they fall between years 2–3 and 3–4. Centring them gives (14.75 + 16.75)/2 = 15.75 for year 3.
Source: Standard method (degree Applied Statistics: time series analysis)
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Under the additive model, the preliminary seasonal effects of the four quarters are +18, −10, +6 and −22; they must be adjusted so that they add up to zero. The quarterly trend is Yc = 300 + 4X, with X in quarters and X = 0 at the first quarter of year 1. What is the forecast for the third quarter of year 4?
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Answer C. 364
The forecast is 364. The preliminary effects add up to −8, so their mean is −2; subtracting −2 (adding 2) from each gives +20, −8, +8 and −20, which add up to zero. The third quarter of year 4 is X = 3 × 4 + 2 = 14, so the trend value is 300 + 4 × 14 = 356. Under the additive model the forecast is 356 + 8 = 364.
Source: Standard method (degree Applied Statistics: time series, additive model and seasonal effects)
6.1Index numbers: construction, tests & cost of livingNotesPractise this chapter · Set 1 free
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Base-year prices of two commodities are ₹2 and ₹5, current-year prices ₹3 and ₹6, base-year quantities 10 and 8, and current-year quantities 10 and 12. What is the Marshall-Edgeworth price index?
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Answer D. 128.57
Marshall-Edgeworth = Σp1(q0 + q1) / Σp0(q0 + q1) × 100 = (3 × 20 + 6 × 20) / (2 × 20 + 5 × 20) × 100 = 180 / 140 × 100 = 128.57.
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Two goods have base-year values (p0q0) of ₹42 and ₹58 and price relatives of 150 and 100. Paasche's price index for the same data is 100. Fisher's ideal price index is
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Answer A. 110
The weighted mean of relatives with weights p0q0 is Laspeyres' index: (63 + 58)/100 × 100 = 121. Fisher = √(121 × 100) = 110.
Source: Standard method (degree-level index numbers)
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For a group of commodities, Laspeyres' quantity index is 110 and the value index (Σp1q1/Σp0q0 × 100) is 165. Paasche's price index is
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Answer C. 150
(Σp1q1/Σp0q1) × (Σp0q1/Σp0q0) = Σp1q1/Σp0q0. So Paasche's price index = value index ÷ Laspeyres' quantity index = 165/1.10 = 150.
Source: Standard method (degree-level index numbers)
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Match List I (formula, × 100) with List II (index):
List I:
A. Σp1q0 / Σp0q0
B. Σq1p0 / Σq0p0
C. Σp1q1 / Σp0q0
D. Σp1q1 / Σp0q1
List II:
1. Value index
2. Laspeyres' price index
3. Paasche's price index
4. Laspeyres' quantity index
Choose the correct answer.
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Answer D. A-2, B-4, C-1, D-3
A is Laspeyres' price index, B is Laspeyres' quantity index, C is the value index and D is Paasche's price index.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
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Consider the following statements about India's official price indices (as of 2026):
1. The all-India Consumer Price Index (Rural, Urban and Combined) is compiled by the National Statistics Office (NSO), MoSPI, and its current series has base year 2024 = 100.
2. The Wholesale Price Index is compiled by the Office of the Economic Adviser, DPIIT, and its current series has base year 2022-23.
3. The Consumer Price Index for Industrial Workers (CPI-IW) is compiled by the NSO with base year 2024 = 100.
Which of the statements given above are correct?
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Answer C. 1 and 2 only
CPI (Rural/Urban/Combined): NSO, MoSPI; base revised from 2012 to 2024 = 100 with the January 2026 index. WPI: Office of the Economic Adviser, DPIIT; base revised from 2011-12 to 2022-23 in June 2026. CPI-IW: Labour Bureau (Ministry of Labour and Employment), base 2016 = 100.
Source: Medha AI; base years from the MoSPI/NSO (CPI 2024 = 100, Feb 2026; IIP 2022-23, 2026), Office of the Economic Adviser, DPIIT (WPI 2022-23, Jun 2026) and Labour Bureau (CPI-IW 2016 = 100) releases, checked Oct 2026
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Assertion (A): A chain base index is preferable when the main interest is in comparing a year's prices with those of the immediately preceding year.
Reason (R): Each link relative compares a year with the year just before it.
Choose the correct answer.
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Answer A. Both A and R are true, and R is the correct explanation of A
Link relatives measure year-to-year change directly, which is why a chain base suits comparisons with the preceding year.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
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Consider the following reasons:
1. The old base year is too distant to be relevant.
2. Two index series with different base years have to be compared.
3. Money values have to be converted into real values.
Which of the above are valid reasons for shifting the base of an index series?
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Answer A. 1 and 2 only
The base is shifted when the old base is too old or abnormal, or to compare series with different bases. Converting money values to real values is deflating.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
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Consider the following possible uses of a consumer price index:
1. Fixing dearness allowance
2. Deflating money wages to find real wages
3. Measuring the purchasing power of money
4. Measuring the correlation between two variables
Which of the above are uses of a consumer price index?
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Answer B. 1, 2 and 3 only
A consumer price index is used to fix dearness allowance, to deflate money wages and to measure the purchasing power of money. It does not measure correlation.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
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Which of the following pairs of index and formula (× 100) is NOT correctly matched?
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Answer D. Dorbish–Bowley – √(Laspeyres × Paasche)
Dorbish–Bowley's index is the arithmetic mean of Laspeyres' and Paasche's indices. The geometric mean of the two is Fisher's ideal index.
Source: Standard definition (degree-level index numbers, as in Telangana B.A./B.Com statistics texts)
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In a cost of living index by the family budget method, the groups food, rent, clothing, fuel and others have weights 50, 20, 10, 10 and 10 and current price indices 180, 150, 200, 120 and 140. A family earned 6,000 rupees a month in the base period. What are the cost of living index and the income needed now to keep the same standard of living?
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Answer D. 166 and 9,960 rupees
The index is 166 and the income needed is 9,960 rupees. CLI = Σ(IW)/ΣW = (9,000 + 3,000 + 2,000 + 1,200 + 1,400)/100 = 16,600/100 = 166. To keep the base-period standard, income must rise in the same proportion as the index. Required income = 6,000 × 166/100 = 9,960 rupees.
Source: Standard method (degree Applied Statistics: index numbers)
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