SSC CGL Statistics – Time Series Analysis – Level 2 · Exam Level · Paper II Sprint

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SSC CGL Statistics – Time Series Analysis – Level 2 · Exam Level · Paper II Sprint – 15 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.  
Values for six years: 5, 8, 11, 9, 12, 15. The 3-yearly moving averages are:

Correct Answer: A [8, 9.33, 10.67, 12]

Explanation:

Answer: 8, 9.33, 10.67, 12. Totals 24, 28, 32, 36 ÷ 3.

2.  
For 10, 14, 18, 16, 20, 24 the first centred 4-yearly moving average (placed against the 3rd year) is:

Correct Answer: B [15.75]

Explanation:

4-year totals 58, 68 → averages 14.5, 17 → centred (14.5 + 17)/2 = 15.75.

3.  
Sales (₹ lakh) for 2020–2024: 20, 24, 26, 27, 33. With origin 2022 and x in years, the least-squares trend line is:

Correct Answer: D [y = 26 + 2.9x]

Explanation:

a = 130/5 = 26; Σxy = −40 − 24 + 0 + 27 + 66 = 29; Σx² = 10; b = 29/10 = 2.9.

4.  
Using the trend y = 26 + 2.9x (origin 2022, x in years), the trend estimate for 2025 is:

Correct Answer: C [34.7]

Explanation:

Answer: 34.7. x = 3: 26 + 8.7 = 34.7.

5.  
A trend equation y = 120 + 6x has origin 2020 (x in years). Shifting the origin to 2024 gives:

Correct Answer: D [y = 144 + 6x]

Explanation:

Replace x by x + 4: 120 + 6(x + 4) = 144 + 6x.

6.  
An annual trend equation (annual totals) is Y = 600 + 72x, origin mid-2023, x in years. The monthly trend equation (x in months) is:

Correct Answer: A [y = 50 + 0.5x]

Explanation:

Divide a by 12 and b by 144: 600/12 = 50; 72/144 = 0.5.

7.  
Two-quantity comparison
Quantity I: sum of 12 monthly seasonal indices
Quantity II: 3 × the sum of 4 quarterly seasonal indices

Correct Answer: C [Quantity I = Quantity II]

Explanation:

Answer: Quantity I = Quantity II. 1,200 = 3 × 400.

8.  
Assertion–Reason
A: A 4-quarter moving average must be centred before it is used as a trend value for a quarter.
R: An even-period moving average falls between two time points.

Correct Answer: B [Both A and R are true and R explains A]

Explanation:

The 4-quarter average sits between Q2 and Q3; averaging two successive ones brings it onto Q3.

9.  
Trick SpotterLeast-squares trend for 6 years (even n). The quickest coding is:

Correct Answer: C [x = 2 × (year − middle point): −5, −3, −1, 1, 3, 5]

Explanation:

Odd multiples make Σx = 0 so a = ȳ and b = Σxy/Σx² (per half-year).

10.  
Spot My Mistake“Trend y = 40 + 3x was fitted with x = −5, −3, −1, 1, 3, 5 (origin 2020.5). So the yearly increase is 3.” The yearly increase is:

Correct Answer: A [6]

Explanation:

x moves 2 units per year, so the yearly change = 2 × 3 = 6.

11.  
Seasonal index of Q2 is 98. The deseasonalised value of Q2 sales of ₹ 1,960 is:

Correct Answer: B [₹ 2,000]

Explanation:

Answer: ₹ 2,000. 1,960 ÷ 98 × 100 = 2,000.

12.  
Under the multiplicative model, the trend value for a quarter is 500 and its seasonal index is 112. The expected (seasonal) value is:

Correct Answer: D [560]

Explanation:

500 × 112/100 = 560 (additive model would ADD a seasonal effect instead).

13.  
Diagram-basedThe quarterly series below repeats the same shape every year with no rise or fall.

It shows mainly:

Correct Answer: B [Seasonal variation only]

Explanation:

Same up-and-down pattern each year, flat level – pure seasonality.

14.  
Odd one outWhich of these is the odd one out among methods of measuring trend?

Correct Answer: D [Method of link relatives]

Explanation:

Link relatives measure seasonal variation, not trend.

15.  
Six yearly values 30, 34, 44, 40, 44, 51 are split into two halves. The semi-averages are:

Correct Answer: C [36 and 45]

Explanation:

(30 + 34 + 44)/3 = 36 and (40 + 44 + 51)/3 = 45, plotted against the 2nd and 5th years.

➤ 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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