For the given values 8, 10, 12, 14, 16; the three-year moving averages are: Option 1: 10, 12, 14 Option 2: 11, 13, 15 Option 3: 16, 14, 18 Option 4: 12, 14, 16

Answer: 10, 12, 14. Solution: Given values: 8, 10, 12, 14, 16 A three-year moving average takes 3 consecutive values, calculates their average, then moves to the next set of 3 values. For the first 3 values: 8, 10, 12 Average = (8 + 10 + 12)/3 = 30/3 = 10 For the next 3 values: 10, 12, 14 Average = (10 + 12 + 14)/3 = 36/3 = 12 For the next 3 values: 12, 14, 16 Average = (12 + 14 + 16)/3 = 42/3 = 14 The three-year moving averages are: 10, 12, 14

Statistics & Applications

Trends & Data

Easy

applied

For the given values 8, 10, 12, 14, 16; the three-year moving averages are:

10, 12, 14

11, 13, 15

16, 14, 18

12, 14, 16

✅ Correct Option: 1

Given values: 8, 10, 12, 14, 16

A three-year moving average takes 3 consecutive values, calculates their average, then moves to the next set of 3 values.

For the first 3 values: 8, 10, 12

Average $= \dfrac{8 + 10 + 12}{3}$

$= \dfrac{30}{3}$

$= 10$

For the next 3 values: 10, 12, 14

Average $= \dfrac{10 + 12 + 14}{3}$

$= \dfrac{36}{3}$

$= 12$

For the next 3 values: 12, 14, 16

Average $= \dfrac{12 + 14 + 16}{3}$

$= \dfrac{42}{3}$

$= 14$

The three-year moving averages are: 10, 12, 14

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 :

2026: 18 May Shift 1

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

2026: 22 May Shift 1

Consider the following data:

Year	1995	1996	1997	1998	1999	2000	2001	2002
Sales (in crores)	6.7	5.3	4.3	6.1	5.6	7.9	5.8	6.1

By using the method of least squares, the trend value for 1997 is :

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:

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: 3 June Shift 2

For the given five values, 16,25,19,34,43, the three year moving averages are

For the given values 8, 10, 12, 14, 16; the three-year moving averages are:

Solution

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