Statistics & Applications

Trends & Data

Easy

applied

For the given five values 15,24,18,33,42, the three years moving averages are

19,22,33

19,25,31

19,30,31

19,25,33

✅ Correct Option: 2

Given values: 15, 24, 18, 33, 42

A 3-year moving average is calculated by taking 3 consecutive values, adding them, and dividing by 3.

With 5 values, there are 3 possible groups of consecutive values.

First group: 15, 24, 18

$MA_1 = \dfrac{15 + 24 + 18}{3}$

$MA_1 = \dfrac{57}{3}$

$MA_1 = 19$

Second group: 24, 18, 33

$MA_2 = \dfrac{24 + 18 + 33}{3}$

$MA_2 = \dfrac{75}{3}$

$MA_2 = 25$

Third group: 18, 33, 42

$MA_3 = \dfrac{18 + 33 + 42}{3}$

$MA_3 = \dfrac{93}{3}$

$MA_3 = 31$

Therefore, the three-year moving averages are: 19, 25, 31

2025: 21 May Shift 1

If for the following data:

Year (x)	2000	2001	2002	2003	2004	2005	2006
Production(in tonnes) (y)	40	45	46	42	47	50	46

the equation of the straight line trend is $y = 45.143 + 1.036(x - 2003)$ , then the trend value for the year 2004 is

2025: 13 May Shift 2

On which of the following components, the pattern and behavior of the data in any time series is based?

(A). Secular trend component

(B). Seasonal component

(C). Cyclical component

(D). Regular component

Choose the correct answer from the options given below:

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?

2026: 29 May Shift 1

If 35, 70, 36, 59, 62 is the given annual time series, then 3-yearly moving averages are

2025: 14 May Shift 1

If $y = a + b(x - 2022)$ is a straight line trend using the least square method for the following data

Year ( $x$ )	2020	2021	2022	2023	2024
Profit (Rs. '000) ( $y$ )	2	3	4	5	2

Then the value of $\frac{a}{b}$ is:

2026: 29 May Shift 1

If for the following data:

Year	2001	2002	2003	2004	2005	2006	2007
Production (in lakh tonnes)	30	35	36	32	37	40	36

Using straight line trend by the method of least squares, the trend value for the year 2009 is :

For the given five values 15,24,18,33,42, the three years moving averages are

Solution

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