Statistics & Applications

Trends & Data

Hard

applied

If 18, Q, 19.2, T, 19.8 are the 5-year moving averages of the following series of observations:

16, P, 20, 18, R, 17, 19, S, 20, then

Match List-I with List-II

List-I List-II
(A) $3P + 2R$ (I) 11.4
(B) $2R - (P+S)$ (II) 86
(C) $\frac{1}{5}(P+R+S)$ (III) 37.6
(D) $Q+T$ (IV) 9

Choose the correct answer from the options given below:

List-I	List-II
(A) $3P + 2R$	(I) 11.4
(B) $2R - (P+S)$	(II) 86
(C) $\frac{1}{5}(P+R+S)$	(III) 37.6
(D) $Q+T$	(IV) 9

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

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

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

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

✅ Correct Option: 3

Each 5-year moving average is the mean of five consecutive terms. From the first, $P+R=36$ ; from the third, $74+R=96$ so $R=22$ and $P=14$ ; from the fifth, $S=21$ . Then $Q=18.2$ and $T=19.4$ . So $3P+2R=86$ (II), $2R-(P+S)=9$ (IV), $\frac15(P+R+S)=11.4$ (I) and $Q+T=37.6$ (III).

2026: 30 May Shift 2

If the following table represents the three yearly moving averages of a data, then the value of $\frac{a+b+c+d}{3}$ is-

Year	Value	3-yearly moving average
1	2
2	a	4
3	6	b
4	8	7
5	c	9
6	12	d
7	11

2025: 13 May Shift 1

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?

2025: 13 May Shift 1

Which of the following statements are correct?

(A) The method of least squares determines the position of the trend line of the given time series.

(B) The trend line is called the line of best fit.

(C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive.

(D) The normal equations of the trend line $y = a + bx$ are $\sum y = na + b \sum x$ and $\sum xy = a \sum x + b \sum x^2$ , where $n$ is the numbers of observations.

Choose the correct answer from the options given below:

2026: 18 May Shift 1

For the given six values 17, 22, 21, 35, 40, 51, the three years moving averages are

2025: 2 June Shift 1

Data available for profit (₹ Thousands) of a company as

Year	2004	2005	2006	2007	2008	2009	2010
Profit(₹ 000)	114	130	126	144	138	156	164

Based on the above data using least square method the trend value for the year '2007' is

2026: 30 May Shift 1

Let $y_t=a+b(x_i-2021)$ be the straight line trend for the following data by least squares method:

Year( $x_i$ )	2018	2019	2020	2021	2022	2023	2024
Production in Lakh tonnes( $y_i$ )	32	34	30	35	38	39	42

the trend value for the year 2025 approximately is:

Solution

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