Statistics & Applications

Trends & Data

Medium

applied

For predicting the straight line trend in the sales of cars (in thousands) on the basis of 5 consecutive years' data, the company makes use of a 3-year moving averages method. If the sales of the cars for respective years are 15, 24, 18, 33 and 42 respectively, then which of the following averages will not be computed?

✅ Correct Option: 3

A 3-year moving average takes any 3 consecutive years of data, adds their sales values, divides by 3 to get the average, then moves forward to repeat with the next set of 3 consecutive years.

The data for 5 consecutive years:

Year 1: 15 (in thousands)

Year 2: 24 (in thousands)

Year 3: 18 (in thousands)

Year 4: 33 (in thousands)

Year 5: 42 (in thousands)

With 5 years of data, only 3 moving averages can be computed.

Moving Average for Years 1, 2, 3:

$\text{Average} = \dfrac{15 + 24 + 18}{3}$

$= \dfrac{57}{3}$

$= 19$

Moving Average for Years 2, 3, 4:

$\text{Average} = \dfrac{24 + 18 + 33}{3}$

$= \dfrac{75}{3}$

$= 25$

Moving Average for Years 3, 4, 5:

$\text{Average} = \dfrac{18 + 33 + 42}{3}$

$= \dfrac{93}{3}$

$= 31$

The moving averages that can be computed are: 19, 25, and 31.

Checking the options:

Option 1: 19 (computed)
Option 2: 25 (computed)
Option 3: 32 (not computed)
Option 4: 31 (computed)

Therefore, 32 is the average that will not be computed.

2026: 19 May Shift 2

For the given five values 10, a, 13, b, 25, the 3-years moving averages are 15, 18, 19. The value of a+b 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:

2026: 15 May Shift 1

Which of the following statements are correct?

A. If $x_1,x_2,x_3,\dots,x_n$ is the given annual time series, then 3-yearly moving averages are $\dfrac{x_1+x_2+x_3}{3},\dfrac{x_2+x_3+x_4}{3},\dots\dots$

B. In the method of the least squares, if $(t_1,y_1),(t_2,y_2),\dots(t_n,y_n)$ denote the time series and $y_t$ are trend values of $y$ , then $\sum(y-y_t)=0$

C. In the method of the least squares, the sum of squares of the deviations of the values of $y$ from their corresponding trend values is least.

D. The rise in prices before Diwali is an example of a cyclical trend.

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?

2025: 13 May Shift 2

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

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?

Solution

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