Statistics & Applications

Trends & Data

Medium

applied

Match List-I with List-II

List-I List-II
Time Series Component Example
(A) Secular Variation (I) Pandemic
(B) Seasonal Variation (II) Recession in business
(C) Cyclic Variation (III) Monthly sale of woolen cloths
(D) Irregular variation (IV) Data regarding National income

Choose the correct answer from the options given below:

List-I	List-II
Time Series Component	Example
(A) Secular Variation	(I) Pandemic
(B) Seasonal Variation	(II) Recession in business
(C) Cyclic Variation	(III) Monthly sale of woolen cloths
(D) Irregular variation	(IV) Data regarding National income

(A) - (I), (B) - (II), (C) - (III), (D) - (IV)

(A) - (IV), (B) - (III), (C) - (II), (D) - (I)

(A) - (III), (B) - (IV), (C) - (II), (D) - (I)

(A) - (II), (B) - (I), (C) - (IV), (D) - (III)

✅ Correct Option: 2

Time series components represent different patterns in data over time.

Secular Variation refers to long-term changes happening gradually over many years or decades. National income data shows gradual growth over extended periods, making it an example of secular variation.

Seasonal Variation refers to patterns that repeat predictably within a year. Monthly sales of woolen cloths follow this pattern, with high sales in winter months and low sales in summer, repeating annually.

Cyclic Variation refers to wavelike fluctuations occurring over several years, typically associated with business cycles. Recessions in business are part of these cycles, where the economy experiences alternating periods of expansion and contraction.

Irregular Variation refers to unpredictable, random shocks that cannot be forecasted. A pandemic is a sudden, unexpected event that causes irregular disruptions to normal patterns.

The correct matching is:

(A) Secular Variation → (IV) National income data

(B) Seasonal Variation → (III) Monthly sale of woolen cloths

(D) Irregular Variation → (I) Pandemic

The answer is: (A) - (IV), (B) - (III), (C) - (II), (D) - (I)

2025: 13 May Shift 1

If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data:

Year $(x)$	2017	2018	2019	2020	2021	2022	2023
Profit (Rs. '000) $(y)$	14	30	26	44	38	56	64

The trend value for the year 2021 by least square method is:

2025: 15 May Shift 1

Year (t)	2010	2011	2012	2013	2014	2015	2016
Sales (in Rs. crores) (y)	6	8	9	11	13	17	20

In reference to the above data, which of the following statements are correct? (where $x = t - 2013$ )

(A) If the equation of the straight line trend is $y = 12 + 2.29 x$ , then the trend value for the year 2017 is 21.16.

(B) If the equation of the straight line trend is $y = 12 + 2.29 x$ , then the trend value for the year 2013 is 11.

(D) If $(t_1, y_2),(t_2, y_2),(t_3, y_3),......,(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t) = 0$ .

Choose the correct answer from the options given below:

2025: 2 June Shift 1

Calculate Three Yearly moving averages for the following data

Year	2016	2017	2018	2019	2020	2021
Production (thousand tonnes)	200	220	231	254	202	243

2026: 22 May Shift 2

A fire in a factory delaying production for some time is:

2025: 3 June Shift 1

Components of Time Series are

(A) Secular Trend Component

(B) Seasonal Component

(D) Cyclical Component

Choose the correct answer from the options given below:

2025: 15 May Shift 1

For predicting the straight line trend in the sales of cars (in thousands) on the basis of 5 consecutive years' data, the company makes use of a 3-year moving averages method. If the sales of the cars for respective years are 15, 24, 18, 33 and 42 respectively, then which of the following averages will not be computed?

Solution

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