Statistics & Applications

Trends & Data

Medium

applied

Consider the following data:

Year( $x_i$ ) 2004 2005 2006 2007 2008 2009 2010
Profit (₹ 000)( $y_i$ ) 26 26 44 42 108 120 166

Using method of least squares, the trend value for year 2004 will be

Year( $x_i$ )	2004	2005	2006	2007	2008	2009	2010
Profit (₹ 000)( $y_i$ )	26	26	44	42	108	120	166

148

124

✅ Correct Option: 1

Shift the origin to 2007 so that $X = -3,-2,\dots,3$ .

Then $\sum y = 532$ giving $a = 76$ , and $\sum XY = 672$ with $\sum X^2 = 28$ , giving $b = 24$ .

The trend line is $y = 76+24X$ ; for 2004, $X = -3$ , so the trend value is $76-72 = 4$ .

2026: 31 May Shift 2

Observe the following table:

Year	2010	2011	2012	2013	2014	2015
Annual Sale	40	50	60	70	80	90

If the three-year moving averages of the above observations are A, B, C, D respectively, then the largest value of the three-year moving averages is :

2026: 12 May Shift 2

Match the components of time series with the examples associated to them.

Match List-I with List-II

List-I	List-II
(A) Secular Trend	(I) Monthly sale of soft drink increases in summer
(B) Seasonal variations	(II) Rise and fall of the share market
(C) Cyclic Variations	(III) Data regarding national income
(D) Irregular Variations	(IV) Sudden fall in crop yield due to floods

Choose the correct answer from the options given below:

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:

2025: 3 June Shift 2

If $(t_1, y_1)$ , $(t_2, y_2)$ ,......, $(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variables $y$ , then

2025: 14 May Shift 1

For the given 5 values, 15, 18, 21, 27,39; the three year moving averages are:

2025: 16 May Shift 1

Which of the following are normal equations to fit a straight line trend y = a + bx by the method of least squares?

Consider the following data: Year(xix_ixi​)2004200520062007200820092010Profit (₹ 000)(yiy_iyi​)26264442108120166 Using method of least squares, the trend value for year 2004 will be

Solution

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CUET Mathematics Past Year Questions (Topic-Wise)

Consider the following data:

Year( $x_i$ ) 2004 2005 2006 2007 2008 2009 2010
Profit (₹ 000)( $y_i$ ) 26 26 44 42 108 120 166

Using method of least squares, the trend value for year 2004 will be