Statistics & Applications

Trends & Data

Easy

applied

In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?

Cyclical component

Irregular component

Seasonal component

Trend component

✅ Correct Option: 4

The question asks which component shows a gradual, long-term shift upward or downward in time series data.

Cyclical Component involves up and down movements that repeat over several years, like economic booms and recessions. This shows repeated fluctuations in both directions rather than a gradual shift in one direction.

Irregular Component represents random, unpredictable changes such as sudden strikes or natural disasters. These are sudden and random events, not gradual shifts.

Seasonal Component consists of regular patterns that repeat every year or season, such as ice cream sales rising in summer and falling in winter. This repeats the same pattern cyclically rather than showing a continuous shift.

Trend Component represents the long-term direction of the data. Examples include population gradually increasing over 20 years or company sales slowly declining over 10 years. This shows gradual movement in one direction over an extended period.

The trend component exhibits gradual shifts to relatively higher or lower values over a long period of time.

Answer: Option 4 - Trend Component

2025: 16 May Shift 1

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection.

Year (x)	Rural Household (y%)	Urban Household (y%)
2020	2	6
2021	3	7
2022	3	9
2023	4	15
2024	5	20

Based on the above data, which of the following statements are correct?

(A) A straight line trend by the method of the least squares for rural Indians is $y^t$ = 3.4 + 0.7 (x - 2022)

(B) A straight line trend by the method of the least squares for urban Indians is $y^t$ = 11.4 + 4.3 (x - 2022)

(D) The forecast for the year 2025 for rural group using the trend equation is 5.5 %.

Choose the correct answer from the options given below:

2025: 26 May Shift 2

Consider the following data

Year (x)	2010	2011	2012	2013	2014
Profit (Rs. in thousands) (y)	10	12	14	16	13

The equation of straight line trend by method of least square for the above data is given by

2025: 21 May Shift 1

For the given five values 18, 25, 20, 36, 49, the three years moving averages are

2025: 22 May Shift 2

The values of ' $a$ ' and ' $b$ ' if the equation of straight line trend by least square method is given by $y = a + bx$ such that $\sum x = 0$ , $\sum y = 84$ , $\sum xy = 108$ , $\sum x^2 = 70$ for 6 observation at are:

2024: 16 May Shift 1

Which of the following are components of a time series ?

(A) Irregular component

(B) Cyclical component

(D) Trend Component

Choose the correct answer from the options given below :

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:

In which of the following, the time series may show the gradual shifts to relatively higher or lower values over a long period of time?

Solution

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