APPSC Paper I · Assistant Statistical Officer Paper II · Topic 10
10 APPSC Paper I Time Series & Index Numbers questions with answers
31 questions from APPSC ASO 2025 Paper II question paper with answers and APPSC ASO Paper II Mock 1 with answers. Try each one, then tap Show answer.
Previous-paper questions are as in the original paper. Medha AI wrote the answers and explanations.
10.1Time series: components, trend & seasonal variationNotes
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Given below are two statements labelled as Assertion (A) and Reasoning (R).
Assertion (A): Ratio to Moving Average Method is the best and widely used method for estimating the seasonal fluctuations in a time series
Reasoning (R): Ratio to Moving Average Method irons out both trend and cyclical components from the indices of seasonal variations.
In the light of above, choose the correct option.
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Answer A. Both A and B are true and R is correct explanation of A.
The ratio-to-moving-average method is regarded as the most satisfactory and widely used method of seasonal indices because the centred moving average removes the trend and cyclical components, leaving the seasonal (and irregular) part. So both are true and R explains A.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q64, final key
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Which of the following does NOT hold for time series?
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Answer D. For data segregated by time, the value of the variable does not change from time to time.
A time series is studied precisely because the variable changes over time; saying its value does not change from time to time is false.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q89, final key
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Which of the following is NOT the utility of time series analysis?
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Answer B. Time series analysis is not restricted to time-dependent data.
Time series analysis by definition deals with data arranged over time, so the claim that it is not restricted to time-dependent data is false and is not a utility. Planning, forecasting and understanding past behaviour are its standard uses.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q92, final key
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Which of the following methods is NOT used in measuring the seasonal variations?
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Answer A. Method of Least Squares
Seasonal indices are measured by simple averages, ratio-to-trend, ratio-to-moving-average and link relatives; the method of least squares is a method of measuring trend.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q94, final key
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Using the method of Least Square in fitting the trend line of the best fit, the sum of the squares of the deviations of actual values from the computed values is always:
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Answer C. least
The least squares line is chosen so that Σ(Y − Yc)^2 is the minimum possible; it is the sum of the plain deviations Σ(Y − Yc) that equals zero.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q95, final key
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Trend, a component of time series, can be studied by using:
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Answer A. Method of moving averages
Secular trend is measured by freehand, semi-averages, moving averages or least squares; ratio to moving average, link relatives and ratio to trend are methods for seasonal indices.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q119, final key
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Consider the following information in two lists A and B:
List A List B (i) Secular Trend (i) Long time fluctuations (ii) Seasonal Variations (ii) Rising trend of population (iii) Cyclical variations (iii) Isolated special occurrences (iv) Irregular variations (iv) Variations within a period of one year Match the List – A with List – B and select the correct option.
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Answer A. A(i)-B(ii), A(ii)-B(iv), A(iii)-B(i), A(iv)-B(iii)
Secular trend is the long-run tendency (rising population); seasonal variation repeats within a year; cyclical variation is long-period oscillation (business cycles); irregular variation comes from isolated special events.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q123, final key
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Consider the following statements:
Statement I: Seasonal variations can occur within a period of one year.
Statement II: Increased demand of woolen cloths during winter is a seasonal variation.
Which of the statements given above is/are correct?
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Answer D. Both the statements I and II are correct
Seasonal variations are regular movements that recur within a year, and higher winter demand for woollens is a textbook example of one.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q125, final key
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The trend of the annual sales of a company is described by the following trend line.
Yc = 30 + 3.6X, this equation when converted to monthly basis becomes:
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Answer A. Yc = 2.5 + 0.025X
Converting annual totals to monthly values with X still in years: a/12 = 30/12 = 2.5 and b/144 = 3.6/144 = 0.025, giving Yc = 2.5 + 0.025X (X in months).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q126, final key
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Below are given figures of production '000's quintals of a sugar factory:
Year 1941 1942 1943 1944 1945 1946 1947 Production 80 90 92 83 94 99 92 The slope of the trend line for the above data is:
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Answer C. 2
Take X = year - 1944 (-3 to 3): Sum X^2 = 28 and Sum XY = -240 - 180 - 92 + 0 + 94 + 198 + 276 = 56, so b = 56/28 = 2.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q127, final key
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The 3-yearly moving averages of a series for 2019 and 2020 are 40 and 42. If the value of the series in 2018 was 36, its value in 2021 was
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Answer C. 42
MA(2019) = (Y18 + Y19 + Y20)/3 = 40 → total 120; MA(2020) = (Y19 + Y20 + Y21)/3 = 42 → total 126. Subtracting: Y21 − Y18 = 6, so Y21 = 42.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Match List I (method of seasonal index) with List II (what each season's figure is expressed as a percentage of):
List I:
A. Simple average method
B. Ratio-to-trend method
C. Ratio-to-moving-average method
D. Link relative method
List II:
1. The figure of the preceding season
2. The centred moving average for that season
3. The trend value obtained by least squares
4. The average of the season averages (grand average)
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Answer A. A-4, B-3, C-2, D-1
Simple average: season average ÷ grand average × 100. Ratio to trend: Y ÷ trend × 100. Ratio to moving average: Y ÷ centred MA × 100. Link relative: current season ÷ previous season × 100.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Consider the following statements about the method of least squares for measuring trend:
1. Trend values can be obtained for every year of the series, including the first and the last.
2. If one more year's figure is added to the data, the whole trend equation has to be worked out again.
Which of the statements given above is/are correct?
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Answer C. Both 1 and 2
A fitted equation gives a trend value for any year (no values are lost as in moving averages), but it is rigid: adding a year means refitting the line.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Match List I (method of measuring trend) with List II (feature):
List I:
A. Freehand method
B. Semi-averages
C. Moving averages
D. Least squares
List II:
1. Data are divided into two equal parts
2. Minimises the sum of squared deviations of actual values from trend values
3. Highly subjective
4. No trend values for some periods at the beginning and the end
Select the correct answer using the code given below.
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Answer A. A-3, B-1, C-4, D-2
Freehand is subjective; semi-averages split data into two halves; moving averages lose values at both ends; least squares minimises Σ(Y − Yc)².
Source: S.P. Gupta, Statistical Methods: Analysis of Time Series (standard B.Com/B.A. text)
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The monthly trend equation of a company's sales (₹ lakh) is Yc = 80 + 1.5X, with origin January 2024 and X in months. The seasonal index for December is 120. The forecast of sales for December 2025 is
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Answer C. 137.4
Months from January 2024 to December 2025 = 23, so trend = 80 + 1.5 × 23 = 114.5. Forecast = 114.5 × 120 ÷ 100 = 137.4.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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The average link relatives of the four quarters are Q1 = 98, Q2 = 106, Q3 = 112 and Q4 = 88. Taking the chain relative of Q1 as 100, the chain relative of Q3 (before trend correction) is
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Answer D. 118.72
Chain relative = link relative × previous chain relative ÷ 100. Q2: 106; Q3: 106 × 112 ÷ 100 = 118.72.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Which method of computing seasonal indices is the most widely used and is generally regarded as the most satisfactory?
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Answer B. Ratio-to-moving-average method
The ratio-to-moving-average method eliminates T × C by the centred moving average before averaging the S × I ratios, so it is the most widely used; its drawback is the loss of values at the ends.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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The seasonal index of the second quarter for a product is 80. This means that sales in the second quarter are typically
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Answer A. 20% below the average quarterly level
Seasonal indices are measured around 100: 80 means the quarter's normal level is 80% of an average quarter, i.e. 20% below it.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
10.1Index numbers: construction, tests & cost of livingNotes
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A major limitation in construction of index numbers is which of the following?
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Answer A. Index numbers are liable to be manipulated by selfish persons to obtain desired results.
Because choice of base year, items, weights and formula is left to the compiler, index numbers can be manipulated to show a desired result, a well-known limitation.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q65, final key
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If Laspeyer’s quantity and Paasche’s quantity index numbers are given as 120.69 and 120.62, then Fisher’s quantity index number is equal to:
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Answer B. 120.65
Fisher's index = sqrt(L × P) = sqrt(120.69 × 120.62) ≈ 120.65 (the geometric mean lies between the two).
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q66, final key
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Which of the following is not the limitation of Index numbers?
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Answer C. These can not be used for wage policy of the government
Index numbers (especially cost of living indices) are in fact used to fix wages and dearness allowance, so the claim that they cannot be used for wage policy is false and is not a limitation. The other three are standard limitations.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q67, final key
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Given below are two statements labelled as Assertion (A) and Reasoning (R).
Assertion (A): Time reversal test was proposed by Irving Fisher.
Reasoning (R): Fisher’s index number satisfies Factor reversal test.
In the light of above, choose the correct option.
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Answer D. Both A and B are true and R is not correct explanation of A.
Irving Fisher proposed the time reversal and factor reversal tests, and his ideal index satisfies both. But Fisher's index satisfying the factor reversal test does not explain who proposed the time reversal test.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q87, final key
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For a particular year, weekly take home pay is 138.10 and consumer price index is 149.8. Then the real weekly wage is approximately equal to:
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Answer A. 92.19
Real wage = (money wage / CPI) × 100 = (138.10 / 149.8) × 100 ≈ 92.19.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q88, final key
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Match the two columns.
Column A Column B 1. Quantity Index I Value Index 2. Index of Industrial Production II (Σp1q1 / Σp1q0) * 100 3. measures the relative changes in total monetary worth of an item III Measures the changes in the quantity of goods manufactured in a factory 4. Paasche's quantity index IV Compilation and publication by Central Statistical Organisation, MOSPI Show answerHide answer
Answer A. 1- III; 2-IV, 3-I; 4-II
A quantity index measures changes in the quantity produced; the IIP is compiled by the CSO (now NSO), MOSPI; the relative change in total money worth is a value index; Paasche's quantity index weights by current prices: Σp1q1/Σp1q0 x 100.
Source: APPSC Assistant Statistical Officer 2025, Paper II (Notification 12/2024), Q118, final key
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From the data below, what is Fisher's ideal price index?
Commodity Base-year price (₹) Base-year quantity Current-year price (₹) Current-year quantity X 10 8 12 5 Y 5 4 8 10 Show answerHide answer
Answer B. 133.87
Laspeyres = 128 / 100 × 100 = 128; Paasche = 140 / 100 × 100 = 140. Fisher = √(L × P) = √(17920) = 133.87.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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Consider the following statements about chain base index numbers:
1. Items can be added or dropped, and weights revised, more easily than in a fixed base index.
2. They are better than fixed base indices for comparing prices over a long period, such as 2005 with 2025.
Which of the statements given above is/are correct?
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Answer A. 1 only
In the chain base method each year's base is the preceding year, so new items and weights can be brought in easily. But link-relative errors cumulate when chained, so for long-period comparisons a fixed base index is preferred.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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A clerk earned ₹24,000 a month when the cost of living index was 120. The index has now risen to 150. What additional monthly allowance does he need to maintain his former standard of living?
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Answer D. ₹6,000
Income needed = present income × new index / old index = 24,000 × 150 / 120 = ₹30,000. Additional allowance = 30,000 − 24,000 = ₹6,000.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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The prices (in ₹) of three commodities in the base year are 10, 20 and 30 and in the current year 12, 25 and 38 respectively. What is the simple aggregative price index for the current year?
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Answer B. 125
Simple aggregative index = Σp1 / Σp0 × 100 = 75 / 60 × 100 = 125.
Source: Standard method; answer and every option computed and checked in Python
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If Laspeyres' price index is 144 and Paasche's price index is 121, what is Fisher's ideal index?
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Answer C. 132
Fisher's index is the geometric mean of Laspeyres and Paasche: √(144 × 121) = 12 × 11 = 132.
Source: Standard method; answer and every option computed and checked in Python
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Using the data below, what is Paasche's price index?
Commodity Base-year price (₹) Base-year quantity Current-year price (₹) Current-year quantity Rice 8 10 10 12 Dal 15 4 18 5 Milk 5 20 6 15 Show answerHide answer
Answer C. 121.95
Paasche P01 = Σp1q1 / Σp0q1 × 100 = (120 + 90 + 90) / (96 + 75 + 75) × 100 = 300 / 246 × 100 = 121.95.
Source: Medha AI, based on BRAOU/APSCHE degree textbooks (ASO Paper II)
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The time reversal test is satisfied when (P01 is the index for period 1 on base 0 and P10 the index for period 0 on base 1, both as ratios):
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Answer B. P01 × P10 = 1
Fisher's time reversal test requires that the index computed forward and the index computed backward be reciprocals: P01 × P10 = 1.
Source: S.C. Gupta & V.K. Kapoor, Fundamentals of Applied Statistics, Index Numbers
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