Statistics & Applications

Trends & Data

Medium

applied

Which of the following statements are TRUE?

(A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends.

(B) The price of stocks in the share market repeats after a definite time interval.

(C) The rise and fall of the share market is an example of a cyclic trend.

(D) The rise in prices before festivals is an example of a irregular trend.

Choose the correct answer from the options given below:

(A) and (D) only

(A), (B) and (C) only

(A) and (C) only

(B), (C) and (D) only

✅ Correct Option: 3

Different types of trends in time series analysis:

Seasonal Trends: Patterns that repeat regularly at specific times (every year, every month, etc.)

Cyclic Trends: Long-term ups and downs with no fixed time period, usually spanning several years

Irregular Trends: Random, unpredictable changes with no pattern

Statement (A): Woolen clothes, gold, silver sales exhibit seasonal trends

This statement is TRUE.

Woolen clothes sell more in winter every year, showing a seasonal pattern.

Gold and silver sales increase during festivals and wedding seasons at predictable times each year, showing a seasonal pattern.

Statement (B): Stock prices repeat after a definite time interval

This statement is FALSE.

Stock prices fluctuate but do not repeat in a fixed pattern. No definite time interval exists for stock price movements.

Statement (C): Rise and fall of share market is a cyclic trend

This statement is TRUE.

Stock markets have boom and bust cycles that go up for years, then crash, then recover. These cycles don't have fixed lengths, which makes them cyclic trends rather than seasonal trends.

Statement (D): Price rise before festivals is an irregular trend

This statement is FALSE.

Prices rising before festivals happens every year and is predictable. This is a seasonal trend, not an irregular trend. Irregular trends are random and unpredictable, but festivals occur at known times.

The TRUE statements are (A) and (C) only.

2026: 30 May Shift 1

In reference to the Time Series Analysis, which of the following statements are correct?

A. Variations which generally occur due to the general tendency of the data to increase or decrease, are known as secular variations.

B. Variations which occur due to change in climate, wheather conditions, festivals etc. are known as seasonal variations.

C. Variations which occur due to some unpredictable forces are known as cyclic variations.

D. Variations which occur due to booms and depressions are known as irregular variations.

Choose the correct answer from the options given below:

2026: 19 May Shift 1

For a certain data $(x_i, y_i)$ , $i = 1,2,...,7$ : $\sum_{i=1}^{7} y_i = 246$ and $\sum_{i=1}^{7} u_iy_i = 29$ , $\sum_{i=1}^{7} u_i^2 = 28$ where $u_i = x_i - 2004$ , then straight line trend by the method of least square is :

2026: 22 May Shift 2

For the given five values 15, 24, 18, 33, 45, which of the following is not the three years moving average?

2025: 30 May Shift 2

A company is shut down due to unavailability of electricity due to non payment of electricity Bill because of some unavoidable circumstances. Under which component of time series does this situation fall?

2025: 15 May Shift 1

The rise in prices before festivals is an example of

2025: 22 May Shift 1

Consider the following data:

Year (X)	2004	2005	2006	2007	2008	2009	2010
Profit (₹) (y)	114	130	126	144	138	156	164

The equation of straight line trend by using least square method is $y = 138.86 + 7.64 (x - 2007)$ , then the trend values for the year 2004 is

Solution

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