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Time series and forecasting - class-XII

Description: time series and forecasting
Number of Questions: 38
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Tags: analyzing data time series and forecasting time series applied statistics maths moving averages business mathematics and statistics statistics
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A train running at $\dfrac{7}{{11}}$ of its own speed reached a place in 22 hours. How much time could be saved if the train would have run at its own speed ?

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. 7 hours

  2. 8 hours

  3. 14 hours

  4. 16 hours

Show answer
Correct Option: B
Explanation:
Let s be the actual speed of the train and d be the distance that needs to be covered to reach that place.

Here, speed$=\dfrac{Distance}{Time}$

As per question,

The train is running at $\dfrac{7}{11}$ of its own speed and reaches the place in $22$ hrs.

$\therefore d=\dfrac{7}{11}s.22$

$\Rightarrow d=14s$ ………..$(1)$

Let t be the time taken by the train to reach the place with its actual speed.

$\therefore d=st$ ………..$(2)$

from $(1)$ and $(2)$, we get

$14s=st$

$\Rightarrow t=14$ hours

$\therefore$ Time that could be saved$=22-14$

$=8$hrs.

The total numbers of squares on a chessboard is

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. $206$

  2. $205$

  3. $204$

  4. $202$

Show answer
Correct Option: C
Explanation:

From Permutation and Combination,


no. of squares of 1x1 $=1^2$
no. of squares of 2x2 $=2^2$
no. of squares of 3x3$=3^2$
.
.
.
no. of squares of 8x8 $=8^2$

Hence Total number of squares $=1^2+2^2+......+8^2$
 $\implies 204$

The average weight of $A,B,C$ is $45kg$ . If the average weight of $A$ and $B$ be $40kg$ and that of $B$ and $C$ be $43kg$, find the weight of $B$ ?

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. $21kg$

  2. $20kg$

  3. $38kg$

  4. $31kg$

Show answer
Correct Option: D
Explanation:

$\cfrac{A+B+C}{3}=45$ $kg$

$\Rightarrow A+B+C=45\times3=135$ $kg$
$\Rightarrow \cfrac{A+B}{2}=40$ $kg$
$\Rightarrow A+B=80$ $kg$
$\therefore C=135-80=55$ $kg$
$\Rightarrow \cfrac{B+C}{2}=43$ $kg$
$\Rightarrow B+C=86$ $kg$
$\therefore B=86-55=31$ $kg$
$\therefore$ The weight of $B$ is $31$ $kg$.

In a call of 100 students there are 70 boys whose average marks in a subject is 75. If the average marks of the complete class is 72 . then the average marks of the girls is 

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. 73

  2. 65

  3. 68

  4. 74

Show answer
Correct Option: B
Explanation:
Total student = 100
For 70 students total marks = 75×7075×70
=5250=5250
Total marks of girls = & 7200-5250$
=1950=1950
Average of girls = 195030195030
=65

.Twelve years hence a man will be four times as he was twelve years ago, then his present age is

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. 20 years

  2. 25 years

  3. 28 years

  4. 30 years

Show answer
Correct Option: A
Explanation:

Let his present age be x
According to problem x + 12 = 4 (x - 12)
-3x = - 48 - 12
3x = 60
x = 20 years

David obtained 76,65,82,67,and 85 marks(out of 100) in English,Mathematics,Physics,Chemistry and Biology.What are his average marks?

statistics moving averages uses of average in day-to-day life moving average and variation simple moving average introduction to time series introduction to time series and forecasting

  1. 75

  2. 69

  3. 72

  4. 76

Show answer
Correct Option: A
Explanation:
Average is equal to the sum of marks of all the subjects by the total number of subjects.

$\therefore Avg=\dfrac{76+65+82+67+85}{5}=75$

Moving-averages:

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. Give the trend in a straight line

  2. Measure the seasonal variations

  3. Smooth-out the time series

  4. None of them

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  Moving-averages : $Smooth-out\,the\,time\,series$.

$\Rightarrow$  A moving average  is a widely used indicator in technical analysis that helps smooth out price action by filtering out the “noise” from random price fluctuations.
$\Rightarrow$  It is a trend-following, or lagging, indicator because it is based on past prices.

The average weight of 10 men is decreased by 3 kg when one of them whose weight is 80 kg is replaced by a new person. The weight of the new person is

statistics moving averages uses of average in day-to-day life moving average and variation simple moving average introduction to time series introduction to time series and forecasting

  1. 70

  2. 60

  3. 50

  4. 73

Show answer
Correct Option: C
Explanation:

Let weight of $9$ men $=x$.

Weight of new men $=y$

According to the question,
$\dfrac{x+80}{10}-3=\dfrac{x+y}{10}$
$\dfrac{x+80-30}{10}=\dfrac{x+y}{10}$
$x+50=x+y$
$y=50\ kg$

Hence, this is the answer.

The problem given below consists  of a question followed by three statements. You have to study the question and the statements and decide which of the statements(s) is / are necessary to answer the question.
How many marks did Tarun secure in English?
(i)The average marks obtained by Tarun in four subjects including English are 60.
(ii) The total marks obtained by him in English and Mathematics together are 170.
(iii)The total marks obtained by him in Mathematics and science together are 180.

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. I and II only

  2. II and III only

  3. I and III only

  4. None of these

Show answer
Correct Option: D
Explanation:

These statements are not enough to find out his English marks. 
So Ans = D

Choose the correct answer from the alternatives given.
A man covers a distance of $160$ km at $64 km/hr$ and next $160$ km at $80 km/hr$. What is his average speed for his whole journey of $320$ km?

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. $73.00km/h$

  2. $71.11km/h$

  3. $70.50km/h$

  4. $72.25km/h$

Show answer
Correct Option: B

Bira and his wife Sheena have two daughters aged $12$ and $16$. Sheena's mother and father, aged $65$ and $72$, also live with them. Bira is currently looking for work, but can't find any. His elder daughter completed class $10$ and prefers to look for work. Sheena prefers to stay at home to look after house works. How many unemployed members does Bira's family have?

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. $1$

  2. $2$

  3. $3$

  4. $4$

Show answer
Correct Option: B
Explanation:

Only Bira and his elder daughter can be called unemployed as per the given situation.

A qualitative forecast

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. predicts the quality of a new product.

  2. predicts the direction, but not the magnitude, of change in a variable.

  3. is a forecast that is classified on a numerical scale from $1$ (poor quality) to $10$ (perfect quality).

  4. is a forecast that is based on econometric methods.

Show answer
Correct Option: B
Explanation:

Qualitative forecast is an estimation methodology which uses expert judgment, rather than numerical analysis. It predicts the direction, but not the magnitude of change in variable.

Two pipes A and B can fill a tank in 20 and 30 minutes respectively. If both the pipes are used together, then how long will it take to fill the tank?

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. $12 min$

  2. $15 min$

  3. $25 min$

  4. $50 min$

Show answer
Correct Option: A
Explanation:

$\displaystyle \frac{1}{20} + \frac{1}{30} = \frac{1}{x}$
$\displaystyle \frac{5}{60} = \frac{1}{x}     \Rightarrow 12 min$

The first step in time-series analysis is to

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. perform preliminary regression calculations.

  2. calculate a moving average.

  3. plot the data on a graph.

  4. identify relevant correlated variables.

Show answer
Correct Option: C
Explanation:

The first step in time series analysis is to plot the data on a graph.

In moving average method, we cannot find the trend values of some:

statistics moving averages moving average and variation simple moving average uses of average in day-to-day life introduction to time series introduction to time series and forecasting

  1. Middle periods

  2. End periods

  3. Starting periods

  4. Between extreme periods

Show answer
Correct Option: D
Explanation:

In moving average method, we cannot find the trend value of some:between extreme periods.

Which of the following is not one of the four types of variation that is estimated in time-series analysis?

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Predictable

  2. Trend

  3. Cyclical

  4. Irregular

Show answer
Correct Option: A
Explanation:

Four types of variations estimated in time-series analysis are :-

1. Trend
2. Seasonal
3. Cyclical
4. Irregular

Hence, A) Predictable is the correct option

The unsystematic sequence which follows irregular pattern of variations is called:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Noise

  2. Signal

  3. Linear

  4. Non-Linear

Show answer
Correct Option: A
Explanation:

By definition,
Noise is a component of time series which is the unsystematic sequence which follows irregular pattern of variations

A time series consists of:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Short-term variations

  2. Long-term variations

  3. Irregular variations

  4. All of the above

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  A time series consist of $Short-term\,variations,\,Long-term\,variations\, and\, Irregular\,variation.$

$\Rightarrow$  $Short \,term\, variation -$ Seasonal trends are short term movements occurring in data due to seasonal factors. For example,  it is commonly observed that the consumption of ice-cream during summer is generally high and hence an ice-cream dealer's sales would be higher in some months of the year while relatively lower during winter months.
$\Rightarrow$  $Long\,term\, variation -$ The secular trend is the main component of a time series which results from long term effects of socio-economic and political factors. Prices and export and import data, for example, reflect obviously increasing tendencies over time.
$\Rightarrow$  $Irregular\,variation-$These are sudden changes occurring in a time series which are unlikely to be repeated. They are components of a time series. Floods, fires, earthquakes, revolutions, epidemics, strikes etc., are the root causes of such irregularities

Depression in business is:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Cyclical

  3. Seasonal

  4. Irregular

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Depression in business is : $Cyclical $.

$\Rightarrow$  Depression phase - The depression or trough is the bottom of a cycle where economic activity remains at a highly low level. Income, employment, output, price level, etc. go down. 
$\Rightarrow$  A depression is generally characterized by high unemployment of labor and capital and a low level of consumer demand in relation to the economy’s capacity to produce. 
$\Rightarrow$  This deficiency in demand forces firms to cut back production and lay-off workers.

An orderly set of data arranged in accordance with their time of occurrence is called:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Arithmetic series

  2. Harmonic series

  3. Geometric series

  4. Time series

Show answer
Correct Option: D
Explanation:

From the definition of Time series,

Time series is an orderly set of data arranged in accordance with their time of occurrence.

Barometric methods are used to forecast

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. seasonal variation.

  2. secular trend.

  3. cyclical variation.

  4. irregular variation.

Show answer
Correct Option: C
Explanation:

Its a fact. Barometric methods are used to forecast cyclical variation.

If $A : B =3 : 4$ and $B : C =5 : 6$, then $A : C$ is

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. $7:3$

  2. $3:4$

  3. $1:2$

  4. $5:9$

Show answer
Correct Option: D
Explanation:

$A:B=3:4$
 $B:C=5:6$
 $\therefore \frac { A }{ B } =\frac { 3 }{ 4 } & \frac { B }{ C } =\frac { 5 }{ 6 } $
 $\therefore \frac { A }{ B } \times \frac { B }{ C } =\frac { A }{ C } $
$\therefore \frac { 3 }{ 4 } \times \frac { 5 }{ 6 } =A:C$
 $=\frac { 15 }{ 24 } =\frac { 5 }{ 8 } $
A:C=5:8

A pattern that is repeated throughout a time series and has a recurrence period of at most one year is called

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Cyclical variation

  2. Irregular variation

  3. Seasonal variation

  4. Long term variation

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  A pattern that is repeated throughout a time series and has a recurrence period of at most one year is called $Seasonal\, variation$.

$\Rightarrow$  The seasonal variations may be due to various seasons or weather conditions for example sale of cold drink would go up in summers & go down in winters.
$\Rightarrow$   These variations may be also due to man-made conventions & due to habits, customs or traditions. For example, sales might go up during Diwali & Christmas or sales of restaurants & eateries might go down during Navratri’s.

Increase in the number of patients in the hospital due to heat stroke is:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Irregular variation

  3. Seasonal variation

  4. Cyclical variation

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  Increase in the number of patients in the hospital due to heat stroke is : $Seasonal\, variation.$

$\Rightarrow$  Over a span of one year, seasonal variation takes place due to the rhythmic forces which operate in a regular and periodic manner. These forces have the same or almost similar pattern year after year.
$\Rightarrow$  It is common knowledge that the value of many variables depends in part on the time of year.
$\Rightarrow$  Increase in number of  Heat stroke is one of example of seasonal variation because it's happens in every year in summer.

A complete cycle consists of a period of:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Prosperity and depression

  2. Prosperity and recovery

  3. Prosperity and recession

  4. Recession and recovery

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  A complete cycle consist of period of : $Prosperity\, and\, recession$.

$\Rightarrow$  $Prosperity\,phase$ : When there is an expansion of output, income, employment, prices and profits, there is also a rise in the standard of living. This period is termed as Prosperity phase.
$\Rightarrow$  $Recession Phase$ : The turning point from prosperity to depression is termed as Recession Phase.
During a recession period, the economic activities slow down. When demand starts falling, the overproduction and future investment plans are also given up. There is a steady decline in the output, income, employment, prices and profits. 

The general pattern of increase or decrease in economics or social phenomena is shown by:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Seasonal trend

  2. Cyclical trend

  3. Secular trend

  4. Irregular trend

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The general pattern of increase or decrease in economics or social phenomena is shown by : $Secular\, trend$.

$\Rightarrow$  Term tendency of the time series to move in an upward or down ward direction. It indicates how on the whole, it has behaved over the entire period under reference.
$\Rightarrow$  These are result of long-term forces that gradually operate on the time series variable. A general tendency of a variable to increase, decrease or remain constant in long term.
$\Rightarrow$  Secular trend is be long-term tendency of the time series to move on upward or downward direction. It indicates how on the whole behaved over the entire period under reference.

Secular trend can be measured by:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Two methods

  2. Three methods

  3. Four methods

  4. Five methods

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  Secular trend can be measured by: $Four\, methods.$

$\Rightarrow$  The four methods are: 
$(1)$  Graphic or a Freehand Curve Method.
$(2)$  Method of Semi Averages.
$(3)$  Method of Moving Averages.
$(4)$  Method of Least Squares.

Damages due to floods, droughts, strikes fires and political disturbances are:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Trend

  2. Seasonal

  3. Cyclical

  4. Irregular

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  Damages due to floods, drought, strikes fires and political disturbances are : $Irregular$.

$\Rightarrow$  Irregular variations which occur on account of random external events.
$\Rightarrow$  These variations either go very deep downward or too high upward to attain peaks abruptly. These fluctuations are a result of unforeseen and unpredictably forces which operate in absolutely random or erratic manner.
$\Rightarrow$  These variations are due to floods, wars, famines, earthquakes, strikes, lockouts, epidemics etc.

The method of moving average is used to find the:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Seasonal variation

  3. Cyclical variation

  4. Irregular variation

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  The method of moving average is used to find the : $Secular\, trend.$

$\Rightarrow$  A moving average is an average (Arithmetic mean) of fixed number of items (known as periods) which moves through a series by dropping the first item of the previously averaged group and adding the next item in each successive average.
$\Rightarrow$   The value so computed is considered the trend value for the unit of time falling at the center of the period used in the calculation of the average.

A complete cycle passes through:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Two stages

  2. Three stages

  3. Four stages

  4. Difficult to tell

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  A complete cycle passes through : $Four\, stages$.

$\Rightarrow$  Four stages are : 

$(1)$  Prosperity Stage : Expansion or Boom or Upswing of economy.
$(2)$  Recession Stage : from prosperity to recession (upper turning point).
$(3)$  Depression Stage : Contraction or Downswing of economy.
$(4)$  Recovery Stage : from depression to prosperity (lower turning Point).

The rise and fall of a time series over periods longer than one year is called

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Seasonal variation

  3. Cyclical variation

  4. Irregular variation

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The rise and fall of time series over periods longer than one year is called $Cyclical\,variation.$

$\Rightarrow$  Cyclical variations, which are also generally termed as business cycles, are the periodic movements. These variations in a time series are due to ups & downs recurring after a period from Season to Season.
$\Rightarrow$   Though they are more or less regular, they may not be uniformly periodic. These are oscillatory movements which are present in any business activity and is termed as business cycle.
$\Rightarrow$  It has got four phases consisting of prosperity (boom), recession, depression and recovery. All these phases together may last from 7 to 9 years may be less or more.

The secular trend is measured by the method of semi-averages when:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Time series based on yearly values

  2. Time series consists of even number of values

  3. Trend is linear

  4. None of them

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  The secular trend is measured by the method of semi-averages when : $Trend\,is\,linear.$

$\Rightarrow$  Under this method the whole time series data is classified into two equal parts and the averages for each half are calculated. If the data is for even number of years, it is easily divided into two.
$\Rightarrow$   If the data is for odd number of years, then the middle year of the time series is left and the two halves are constituted with the period on each side of the middle year.
$\Rightarrow$  The arithmetic mean for a half is taken to be representative of the value corresponding to the midpoint of the time interval of that half. Thus we get two points. 

$\Rightarrow$  These two points are plotted on a graph and then are joined by straight line which is our required trend line.

Increased demand of admission in the subject of computer in Pakistan is:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Cyclical trend

  3. Seasonal trend

  4. Irregular trend

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Increased demand of admission in the subject of computer in Pakistan is : $Secular\, trend$.

$\Rightarrow$  Secular trend is be long-term tendency of the time series to move on upward or downward direction.
$\Rightarrow$  It indicates how on the whole behaved over the entire period under reference. These are result of long term forces that gradually operate on the time series variable.
$\Rightarrow$  Most of the time series relating to Economic, Business and Commerce might show an upward tendency in case of population, production & sales of products, incomes, prices; or downward tendency might be noticed in time series relating to share prices, death, birth rate etc. due to global melt down, or improvement in medical facilities etc. All these indicate trend.

The fire in a factory is an example of

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Secular trend

  2. Seasonal movements

  3. Cyclical variations

  4. Irregular variations

Show answer
Correct Option: D
Explanation:

$\Rightarrow$  The fire in factory is an example of $Irregular\, variations.$

$\Rightarrow$  Irregular variations which occur on account of random external events.
$\Rightarrow$ These variations either go very deep downward or too high upward to attain peaks abruptly.
$\Rightarrow$  They do not have any definite pattern and it cannot be predicted in advance. These variations are due to floods, wars, famines, earthquakes, strikes, lockouts, epidemics etc.

Wheat crops badly damaged on account of rains is

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Cyclical movement

  2. Random movement

  3. Secular trend

  4. Seasonal movement

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Wheat crops badly damaged on account of rains is $Random\, movement$

$\Rightarrow$  Random movement which occur on account of irregular external events.
$\Rightarrow$  These variations either go very deep downward or too high upward to attain peaks abruptly. These fluctuations are a result of unforeseen and unpredictably forces which operate in absolutely random or erratic manner.
$\Rightarrow$  They do not have any definite pattern and it cannot be predicted in advance. These variations are due to floods, wars, famines, earthquakes, strikes, lockouts, epidemics etc.

Moving average method is used for measurement of trend when:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Trend is linear

  2. Trend is non linear

  3. Trend is curvilinear

  4. None of them

Show answer
Correct Option: A
Explanation:

$\Rightarrow$  Moving average method is used for measurement of trend when : $Trend\, is\,linear$.

$\Rightarrow$  In the method of moving average, successive arithmetic averages are computed from overlapping groups of successive values of a time series. Each group includes all the observations in a given time interval,termed as the period of moving average.
$\Rightarrow$  The next group is obtained by replacing the oldest value by thenext value in the series. The averages of such groups are known as the moving averages. The moving averages of a group are always shown at the center of its period.

In time series seasonal variations can occur within a period of:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Four years

  2. Three years

  3. One year

  4. Nine years

Show answer
Correct Option: C
Explanation:

$\Rightarrow$  In time series seasonal variations can occur within a period of : $One\,year$.

$\Rightarrow$  Over a span of one year, seasonal variation takes place due to the rhythmic forces which operate in a regular and periodic manner. These forces have the same or almost similar pattern year after year.
$\Rightarrow$  The seasonal variations may be due to various seasons or weather conditions for example sale of cold drink would go up in summers & go down in winters.

Indicate which of the following an example of seasonal variations is:

business mathematics and statistics moving averages introduction to time series introduction to time series and forecasting time series and forecasting uses of average in day-to-day life

  1. Death rate decreased due to advance in science

  2. The sale of air condition increases during summer

  3. Recovery in business

  4. Sudden causes by wars

Show answer
Correct Option: B
Explanation:

$\Rightarrow$  Example of seasonal variation is : $The\,sale\,of\,air\,condition\,increases\,during\,summer.$

$\Rightarrow$  Over a span of one year, seasonal variation takes place due to the rhythmic forces which operate in a regular and periodic manner. These forces have the same or almost similar pattern year after year.
$\Rightarrow$  The seasonal variations may be due to various seasons or weather conditions.
$\Rightarrow$  These variations may be also due to man-made conventions & due to habits, customs or traditions.

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