Statistics & Applications

Trends & Data

Medium

applied

Consider the following data of expenses (in lakhs) of an organization year wise

Year 2001 2002 2003 2004 2005
Expenses (Rs. lakh) 160 185 220 300 510

Then expected expenses trends for the year 2006 using method of least square is:

Year	2001	2002	2003	2004	2005
Expenses (Rs. lakh)	160	185	220	300	510

Rs. 419.5 lakh

Rs. 620.5 lakh

Rs. 319.5 lakh

Rs. 519.5 lakh

✅ Correct Option: 4

To find the trend line that best fits the expense data, the years are coded to simplify calculations. Using 2003 as the middle year (coded as 0), the coding is: -2, -1, 0, 1, 2.

Year	X (Coded)	Y (Expenses in lakhs)	XY	X²
2001	-2	160	-320	4
2002	-1	185	-185	1
2003	0	220	0	0
2004	1	300	300	1
2005	2	510	1020	4

$\Sigma X = 0$

$\Sigma Y = 1375$

$\Sigma XY = 815$

$\Sigma X^2 = 10$

The trend line equation is $Y = a + bX$ where:

$b = \dfrac{\Sigma XY}{\Sigma X^2}$

$b = \dfrac{815}{10}$

$b = 81.5$

$a = \dfrac{\Sigma Y}{n}$

$a = \dfrac{1375}{5}$

$a = 275$

Therefore, the trend line equation is:

$Y = 275 + 81.5X$

For the year 2006, continuing the coding pattern gives $X = 3$ .

$Y = 275 + 81.5(3)$

$Y = 275 + 244.5$

$Y = 519.5$

The expected expenses for 2006 is Rs. 519.5 lakh.

2025: 13 May Shift 1

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table

Date	1	2	3	4	5	6	7
Number of cases	2	0	5	12	20	27	46

The 3-day moving averages are:

2025: 21 May Shift 2

Let $y = 138.86 + 7.64(x - 2021)$ be a straight line of best fit by using least square method to the following data:

Year(x)	2018	2019	2020	2021	2022	2023	2024
Profit(y) (in Rs. '000)	114	130	126	144	138	156	164

Then the trend value for the year 2024 is:

2025: 26 May Shift 2

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:

2026: 18 May Shift 1

If for the following data:

Year ( $x_i$ )	2010	2011	2012	2013	2014	2015	2016
Sales (in ₹ crores) ( $y_i$ )	6	8	9	11	13	17	20

If the equation of the straight line trend is $y=a+b(x_i-2013)$ , then the trend value for the year 2018 is

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

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 :

Consider the following data of expenses (in lakhs) of an organization year wise Year20012002200320042005Expenses (Rs. lakh)160185220300510 Then expected expenses trends for the year 2006 using method of least square is:

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following data of expenses (in lakhs) of an organization year wise

Year 2001 2002 2003 2004 2005
Expenses (Rs. lakh) 160 185 220 300 510

Then expected expenses trends for the year 2006 using method of least square is: