SSC CGL Statistics – Time Series Analysis – Level 3 · Challenge
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Growth factor b = 10 0.0792 ≈ 1.20, i.e.
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SSC CGL Statistics – Time Series Analysis – Level 3 · Challenge – 8 questions, subject: Statistics (Tier II Paper II). Every question has the correct answer with a one-line explanation; tap "Show Answer". Free practice for TNPSC, UPSC, SSC, Bank and RRB exams – Shanmugam IAS Academy, Coimbatore.
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1.
Average ratios-to-moving-average for Q1–Q4 are 108, 96, 84 and 108 (total 396). The adjusted seasonal index for Q1 is about:
Correct Answer: A [109.09]
Explanation:
Multiply by 400/396: 108 × 400/396 ≈ 109.09.
2.
A 3-period moving average is applied to a series with a linear trend plus a seasonal pattern of period 3 whose effects add to 0. The moving averages:
Correct Answer: D [Reproduce the trend exactly]
Explanation:
Each 3-term window contains one full cycle (sum 0) and averages a linear trend to its middle value: (a + b(t − 1) + a + bt + a + b(t + 1))/3 = a + bt.
3.
Statement-basedWhich of the statements are correct?
I. Moving averages can distort a series whose cycle length differs from the period of the average.
II. The least-squares line passes through the point (x̄, ȳ).
III. Semi-averages are unaffected by extreme values.
I. Moving averages can distort a series whose cycle length differs from the period of the average.
II. The least-squares line passes through the point (x̄, ȳ).
III. Semi-averages are unaffected by extreme values.
Correct Answer: A [Only I and II]
Explanation:
I and II are true. III is false: semi-averages are simple means, so extremes do affect them.
4.
Four years 2021–2024 with values 12, 15, 19, 22 are coded x = −3, −1, 1, 3. The least-squares line is y = 17 + 1.7x. The annual rate of increase is:
Correct Answer: C [3.4]
Explanation:
x changes by 2 per year: 2 × 1.7 = 3.4.
5.
Additive model: trend for a quarter is 820 and the seasonal effect of that quarter is −35. The estimated value is:
Correct Answer: B [785]
Explanation:
Additive: T + S = 820 − 35 = 785.
6.
Quarterly seasonal indices are 115, 95, 80 and 110. A firm's Q3 sales are ₹ 3,200. If there were no seasonal effect, Q3 sales would be:
Correct Answer: B [₹ 4,000]
Explanation:
Answer: ₹ 4,000. 3,200 ÷ 80 × 100 = 4,000.
7.
Arrange in orderArrange the steps of the ratio-to-moving-average method in order:
(i) average the ratios quarter-wise (ii) centred 4-quarter moving averages (iii) adjust the averages to total 400 (iv) express each value as % of its moving average
(i) average the ratios quarter-wise (ii) centred 4-quarter moving averages (iii) adjust the averages to total 400 (iv) express each value as % of its moving average
Correct Answer: C [(ii), (iv), (i), (iii)]
Explanation:
Smooth → ratio → average → adjust.
8.
An exponential trend log y = 1 + 0.0792x (log base 10, x in years) is fitted to output. The output grows each year by about:
Correct Answer: D [20%]
Explanation:
Growth factor b = 10 0.0792 ≈ 1.20, i.e.
➤ Full notes, shortcuts and every answer explained – SSC CGL 2026 Statistics (Tier II Paper II) book (₹149): www.shanmugamiasacademy.in/study-materials/ssc-cgl-statistics
📘 SSC CGL 2026 – Statistics (Tier II Paper II)
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