A set of observations recorded at an equal interval of time is called.
- AArray data
- BData
- CGeometric Series
- ✓Time series data
Answer: D.
View full solution →Question types
Time Series Analysis question types
40 questions across 5 question groups — pick any mix to generate a Applied Maths paper with step-by-step answer keys.
40
Questions
5
Question groups
5
Question types
01
MCQ
15 Q→022 Marks Questions
12 Q→033 Marks Question
5 Q→045 Marks Questions
5 Q→05Case study (4 Marks)
3 Q→Sample Questions
Time Series Analysis questions
One sample from each question group in this chapter. Select any group above to see the full set with answer keys.
In the measurement of the secular trend, the moving averages:
- ✓Smooth out the time series
- BGiven the trend in a straight line
- CMeasure the seasonal Variations
- DNone of the above
Answer: A.
View full solution →In the theory of time series, shortage of certain consumer goods before the annual budget is due to
- ✓Seasonal Variation
- BSecular Trend
- CIrregular Variations
- DCyclic Variation
Answer: A.
View full solution →Prosperity, Recession, and depression in a business is an example of:
- AIrregular Trend
- BSecular Trend
- ✓Cyclical Trend
- DSeasonal Trend
Answer: C.
View full solution →The following are the movement(s) in the secular trend.
- ASmooth
- BRegular
- CSteady
- ✓All of these
Answer: D.
View full solution →Read the following text and answer the following questions on the basis of the same:
Researchers have found a strong correction between attendance for school and academic performance and success. Children that miss school frequently often fall behind-both academically as well as professionally. Absence from school is often the biggest single cause of poor performance and achievement. As a parent, it is crucial to convey the importance of regular attendance to our child and how missing out can damage their future. The table given below shows the daily attendance in thousands at a certain school over a period of two weeks:
Q. 1. Calculate seven days moving averages.
Q. 2. Draw the graphs for moving averages.
Researchers have found a strong correction between attendance for school and academic performance and success. Children that miss school frequently often fall behind-both academically as well as professionally. Absence from school is often the biggest single cause of poor performance and achievement. As a parent, it is crucial to convey the importance of regular attendance to our child and how missing out can damage their future. The table given below shows the daily attendance in thousands at a certain school over a period of two weeks:
| Week 1: | 52 | 48 | 64 | 68 | 52 | 70 | 72 |
| Week 2: | 55 | 47 | 61 | 65 | 58 | 75 | 81 |
Q. 2. Draw the graphs for moving averages.
Read the following text and answer the following questions on the basis of the same:
Strikes is a very powerful weapon used by trade unions and other labour associations to get their demand accepted. It generally involves quitting of work by a group of workers for the purpose of bringing the pressure on their employer so that their demands get accepted. When workers collectively cease to work in a particular industry, they are said to be on strike.
The table give below shows the average number in lakhs, of working days lost in strikes during each year of period 2009-2018 was
Q.1. Calculate three yearly moving average.
Q.2. Draw the graphs for moving averages.
Strikes is a very powerful weapon used by trade unions and other labour associations to get their demand accepted. It generally involves quitting of work by a group of workers for the purpose of bringing the pressure on their employer so that their demands get accepted. When workers collectively cease to work in a particular industry, they are said to be on strike.
The table give below shows the average number in lakhs, of working days lost in strikes during each year of period 2009-2018 was
Q.1. Calculate three yearly moving average.
Q.2. Draw the graphs for moving averages.
What causes secular trend ?
Write down the models of Time Series Analysis.
Define secular trend and seasonal variations.
Fit a straight line trend by the method of least square to the following data on sales (in lakhs) for the period 2011-2018.
| Year | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
| Sales (₹ lakhs) | 76 | 80 | 130 | 144 | 138 | 120 | 174 | 190 |
Fit a straight line trend by the method of least squares to the data given below:
| Year | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
| Sales ( in tones) | 9 | 11 | 13 | 12 | 14 | 15 | 17 |
Explain the method of fitting a straight line.
The following figures relate to the profits of a commercial concern for 8 years.
Find the trend of profits by the method of three-yearly moving averages
| Year | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 |
| Profit (₹) | 15420 | 15470 | 15520 | 21020 | 26500 | 31950 | 35600 | 34900 |
From the following time series obtain trend value by 3 yearly moving averages.
| Year | Sales (in ₹ 000) | Year | Sales (in ₹ 000) |
| 2008 | 8 | 2014 | 16 |
| 2009 | 12 | 2015 | 17 |
| 2010 | 10 | 2016 | 14 |
| 2011 | 13 | 2017 | 17 |
| 2012 | 15 | ||
| 2013 | 12 |
Below are given the figures of production (in m. tonnes) of a rice factory:
(i) Fit the straight line trend to these figures and calculate trend values.
(ii) Estimate the likely sales of the company during 2019.
| Year | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 |
| Production (in m. tonnes) | 80 | 90 | 92 | 83 | 94 | 99 | 92 |
(ii) Estimate the likely sales of the company during 2019.
From the following data calculate the 4- yearly moving averages and determine the trend values
| Years | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 |
| Value | 50.0 | 36.5 | 43.0 | 44.5 | 38.9 | 38.9 | 32.6 | 41.7 | 41.4 | 33.8 |
Calculate four-Yearly moving averages of number of students studying in a higher secondary school in a particular city from the following data.
| Year | Number of Students |
| 2011 | 124 |
| 2012 | 120 |
| 2013 | 135 |
| 2014 | 140 |
| 2015 | 145 |
| 2016 | 158 |
| 2017 | 162 |
| 2018 | 170 |
| 2019 | 175 |
Calculate trend values from the following data assuming 5- yearly and 7- yearly moving average
| Year | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 |
| Value | 110 | 104 | 98 | 105 | 109 | 120 | 115 | 110 |
| Year | 9 | 10 | 11 | 12 | 13 | 14 | 15 | 16 |
| Value | 114 | 122 | 130 | 127 | 122 | 118 | 130 | 140 |
Fit the straight line trend to the following time series data:
Also, tabulate the trend values
| Year | 2017 | 2018 | 2019 | 2020 | 2021 |
| Sale of sugar (in thousand kg) | 80 | 90 | 92 | 83 | 94 |
Read the following text and answer the following questions on the basis of the same:
The following data shows the percentage of rural, urban and suburban Indians who have a high speed internet connection at home:
Q. 1. A straight line trend by the method of least square for the Rural Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 2. A straight line trend by the method of least square for the Urban Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 3. A straight line trend by the method of least square for the Suburban Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 4. What is the forecast for the year 2022 for urban group using trend equation?
(A) 58.6% (B) 43.7% (C) 37.2% (D) 27.2%
View full solution →The following data shows the percentage of rural, urban and suburban Indians who have a high speed internet connection at home:
| Year (t) | Rural | Urban | Suburban |
| 2017 | 3 | 9 | 9 |
| 2018 | 6 | 18 | 17 |
| 2019 | 9 | 21 | 23 |
| 2020 | 16 | 29 | 29 |
| 2021 | 240 | 380 | 40 |
Q. 1. A straight line trend by the method of least square for the Rural Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 2. A straight line trend by the method of least square for the Urban Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 3. A straight line trend by the method of least square for the Suburban Indians is:
(A) $y_t=11.6+5.2 x$
(B) $y_t=23+6.9 x$
(C) $y_t=23.6+7.4 x$
(D) $y_t=13.2+4.5 x$
Q. 4. What is the forecast for the year 2022 for urban group using trend equation?
(A) 58.6% (B) 43.7% (C) 37.2% (D) 27.2%
Read the following text and answer the following questions on the basis of the same:
Today in class Mr. Agarwal is teaching the Method of Least Squares to measure the trend in time series. After explaining the method, he had taken an example which is as follows:
Given below are the data relating to the sales of a product in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.
To solve the given example, he constructed the following table:
Computation of trend values by the method of least squares.
Here, n = 8 (even)
So, origin is mean of two middle years
i.e. $\frac{2018+2019}{2}=2018.5$
Q. 1. If the straight line is $y_t=a+b x$, then value of ' $a$ ' is:
(A) 5.615 (B) 5.759 (C) 5.829 (D) 5.975
Q. 2. If the straight line is $y_t=a+b x$, then value of 'b' is:
(A) 0.051 (B) 0.011 (C) 0.411 (D) None of these
Q. 3. The trend equation is:
(A) $y_t=5.975+0.051 x$
(B) $y_t=0.051+5.975 x$
(C) $y_t=5.975-0.051 x$
(D) None of the above
Q. 4. The trend value for year 2015 is:
(A) 5.691 (B) 5.618 (C) 5.987 (D) 5.719
View full solution →Today in class Mr. Agarwal is teaching the Method of Least Squares to measure the trend in time series. After explaining the method, he had taken an example which is as follows:
Given below are the data relating to the sales of a product in a district.
Fit a straight line trend by the method of least squares and tabulate the trend values.
| Year | 2015 | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 |
| Sales | 6.7 | 5.3 | 4.3 | 6.1 | 5.6 | 7.9 | 5.8 | 6.1 |
Computation of trend values by the method of least squares.
| Years (t) | Sales (y) | x = $\frac{(t-2018.5)}{0.5}$ | XY | $x^2$ |
| 2015 | 6.7 | -7 | -46.9 | 49 |
| 2016 | 5.3 | -5 | -26.5 | 25 |
| 2017 | 4.3 | -3 | -12.9 | 9 |
| 2018 | 6.1 | -1 | -6.1 | 1 |
| 2019 | 5.6 | 1 | 5.6 | 1 |
| 2020 | 7.9 | 3 | 23.7 | 9 |
| 2021 | 5.8 | 5 | 29.0 | 25 |
| 2022 | 6.1 | 7 | 42.7 | 49 |
So, origin is mean of two middle years
i.e. $\frac{2018+2019}{2}=2018.5$
Q. 1. If the straight line is $y_t=a+b x$, then value of ' $a$ ' is:
(A) 5.615 (B) 5.759 (C) 5.829 (D) 5.975
Q. 2. If the straight line is $y_t=a+b x$, then value of 'b' is:
(A) 0.051 (B) 0.011 (C) 0.411 (D) None of these
Q. 3. The trend equation is:
(A) $y_t=5.975+0.051 x$
(B) $y_t=0.051+5.975 x$
(C) $y_t=5.975-0.051 x$
(D) None of the above
Q. 4. The trend value for year 2015 is:
(A) 5.691 (B) 5.618 (C) 5.987 (D) 5.719
Read the following text and answer the following questions on the basis of the same:
The trend equation can be considered as $y_t=a+b x$.
Q. 1. The value of 'a' in the trend equation is:
(A) 138.86 (B) 7.64 (C) 183.86 (D) 7.46
Q. 2. The value of 'b' in the trend equation is:
(A) 138.86 (B) 7.64 (C) 183.86 (D) 7.46
Q. 3. The trend equation is:
(A) $y_t=138.86+7.64 x$
(B) $y_1=7.64+138.86 x$
(C) $y_t=138.86-7.64 x$
(D) None of these
Q. 4. The trend value for year 2015 is:
(A) 161.78 (B) 154.14 (C) 115.94 (D) 138,86
View full solution →| Year (t) | Profit (y) | x = $t_i-$2018 | $x^2$ | xy |
| 2015 | 114 | -3 | 9 | -342 |
| 2016 | 130 | -2 | 4 | -260 |
| 2017 | 126 | -1 | 1 | -126 |
| 2018 | 144 | 0 | 0 | 0 |
| 2019 | 138 | 1 | 1 | 138 |
| 2020 | 156 | 2 | 4 | 312 |
| 2021 | 164 | 3 | 9 | 492 |
Q. 1. The value of 'a' in the trend equation is:
(A) 138.86 (B) 7.64 (C) 183.86 (D) 7.46
Q. 2. The value of 'b' in the trend equation is:
(A) 138.86 (B) 7.64 (C) 183.86 (D) 7.46
Q. 3. The trend equation is:
(A) $y_t=138.86+7.64 x$
(B) $y_1=7.64+138.86 x$
(C) $y_t=138.86-7.64 x$
(D) None of these
Q. 4. The trend value for year 2015 is:
(A) 161.78 (B) 154.14 (C) 115.94 (D) 138,86
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