Statistics & Applications

Trends & Data

Medium

applied

For the given values 27, 35, 42, 45, 51, 34, 43; the five yearly moving averages are:-

38, 40, 42

40, 41.4, 43

41.5, 42, 45

42, 44, 45.3

✅ Correct Option: 2

Given values: 27, 35, 42, 45, 51, 34, 43

A 5-yearly moving average takes 5 consecutive values and finds their average, then moves one position forward and repeats.

With 7 values and groups of 5, there are 3 moving averages possible.

First 5 values: 27, 35, 42, 45, 51

Average $= \dfrac{27 + 35 + 42 + 45 + 51}{5}$

$= \dfrac{200}{5}$

$= 40$

Next 5 values: 35, 42, 45, 51, 34

Average $= \dfrac{35 + 42 + 45 + 51 + 34}{5}$

$= \dfrac{207}{5}$

$= 41.4$

Last 5 values: 42, 45, 51, 34, 43

Average $= \dfrac{42 + 45 + 51 + 34 + 43}{5}$

$= \dfrac{215}{5}$

$= 43$

The three five-yearly moving averages are: 40, 41.4, 43

2025: 3 June Shift 1

Components of Time Series are

(A) Secular Trend Component

(B) Seasonal Component

(D) Cyclical Component

Choose the correct answer from the options given below:

2026: 15 May Shift 1

For the following data:

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

The equation of the straight line trend is $y = a + b(x_i - 2007)$ , then the trend value for the year 2011 is

2026: 12 May Shift 2

For the values 22, 25, 28, 31, 40, 43, the three yearly moving averages are

2025: 14 May Shift 1

Which of the following are correct?

(A) Time series analysis does not help to understand the behavior of a variable in the past.

(B) Time series predict the future behavior of variable.

(D) The main aim of the time series analysis is to derive conclusions after arranging the time series in a systematic manner.

Choose the correct answer from the options given below:

2025: 13 May Shift 2

When data of the variable is collected at distinct time intervals for a specified period of time, it is called

2025: 19 May Shift 1

The following data shows the percentage of urban Indian households who have a high speed 5G internet connection:

Year (x)	2020	2021	2022	2023	2024
Urban house hold (y)	9%	18%	21%	29%	38%

If a straight line trend by the method of least square for the above data is $y = 23 + 6.9(x - 2022)$ , then the forecast for the year 2025 is:

For the given values 27, 35, 42, 45, 51, 34, 43; the five yearly moving averages are:-

Solution

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