CUET Mathematics Statistics & Applications > Trends & Data PYQs

The break-even point is the level of production where

If $(t_1, y_1)$, $(t_2, y_2)$,......,$(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variables $y$, then

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

Assuming the same rate of change continues for the following data: | Year (x) | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---| | Profit(in Percentage) (y) | 38 | 40 | 65 | 72 | 69 | The equation of the straight line trend using the least square method is:

Which of the following statements are TRUE? (A) The sales of woolen clothes, gold, silver etc. exhibit seasonal trends. (B) The price of stocks in the share market repeats after a definite time interval. (C) The rise and fall of the share market is an example of a cyclic trend. (D) The rise in prices before festivals is an example of a irregular trend. Choose the correct answer from the options given below:

Components of Time Series are (A) Secular Trend Component (B) Seasonal Component (C) Moving Average Component (D) Cyclical Component Choose the **correct** answer from the options given below:

Based on the data available for the production ($y_i$ in thousand tons) of a cloth factory for 7 years ($x_i$) using the method of least squares, the straight line trend is given by $y - a + bx$ with $\sum y_i = 608, \sum x_i = 0, \sum x_iy_i = 116, \sum x_i^2 = 28$. Then, the increase in production per year is:

The first m-year moving average of the data 10, 20, 30, 40, 50 is 30. The value of m is

Match List-I with List-II | List-I | List-II | |---|---| | (A) A fire in a factory causing production delay for some time is | (I) Secular trend | | (B) Technological progress is | (II) Seasonal trend | | (C) The rise in prices before big festival is example of | (III) Irregular trend | | (D) Rise and fall of share market is | (IV) Cyclic trend | Choose the correct answer from the options given below:

Calculate Three Yearly moving averages for the following data | Year | 2016 | 2017 | 2018 | 2019 | 2020 | 2021 | |---|---|---|---|---|---|---| | Production (thousand tonnes) | 200 | 220 | 231 | 254 | 202 | 243 |

Data available for profit (₹ Thousands) of a company as | Year | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit(₹ 000) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | Based on the above data using least square method the trend value for the year '2007' is

For the given five values, 3.6, 4.3, 4.3, 3.4, 4.4, the three years moving averages are:

A company is shut down due to unavailability of electricity due to non payment of electricity Bill because of some unavoidable circumstances. Under which component of time series does this situation fall?

Consider the following data: | Year (x) | 2010 | 2011 | 2012 | 2013 | 2014 | |---|---|---|---|---|---| | Sale (in crore Rs.) (y) | 9 | 18 | 21 | 29 | 38 | A straight line trend by the method of least square is:

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

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

Consider the following data of expenses (in lakhs) of an organization year wise | Year | 2001 | 2002 | 2003 | 2004 | 2005 | |---|---|---|---|---|---| | Expenses (Rs. lakh) | 160 | 185 | 220 | 300 | 510 | Then expected expenses trends for the year 2006 using method of least square is:

The rise in prices before Diwali is an example of

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

In the below mentioned demand supply curve , identify the equilibrium point <img src="https://balti.afterboards.in/i1NTrXv1OfbKrI0" width="300px"/>

The five month moving averages for the following data | Month ($r^{th}$) | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | |---|---|---|---|---|---|---|---|---|---| | Actual Demand | 105 | 106 | 110 | 110 | 114 | 121 | 130 | 128 | 137 | is:

Match List-I with List-II | List-I | List-II | |---|---| | (Example) | (Components of Time Series) | | (A) Lockouts and strikes | (I) Secular trend | | (B) Rise and fall of share market | (II) Seasonal trend | | (C) Continuous decline in death rate | (III) Irregular trend | | (D) The rise in prices before Diwali | (IV) Cyclical trend | Choose the correct answer from the options given below:

Consider the following data | Year (x) | 2014 | 2016 | 2018 | 2020 | 2022 | 2024 | |---|---|---|---|---|---|---| | Profit (in Rs. Thousand) (y) | 7 | 9 | 10 | 12 | 14 | 14 | Then for the above data the equation of straight line trend by method of least square is given by:

Match List-I with List-II | List-I | List-II | |---|---| | Time Series Component | Example | | (A) Secular Variation | (I) Pandemic | | (B) Seasonal Variation | (II) Recession in business | | (C) Cyclic Variation | (III) Monthly sale of woolen cloths | | (D) Irregular variation | (IV) Data regarding National income | Choose the correct answer from the options given below:

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

Match List-I with List-II | List-I | List-II | |---|---| | **Example** | **Time-series component** | | (A) Labour strike | (I) Secular-trend | | (B) Continuous decline in death rate | (II) Seasonal | | (C) Rise in prices before Diwali | (III) Cyclical | | (D) Rise and fall of the share-market | (IV) Irregular | Choose the **correct** answer from the options given below:

If three year moving averages for five data items given by 16, 18, 20, 10, 21 are $x$, $y$ and $z$ respectively, then:

The values of '$a$' and '$b$' if the equation of straight line trend by least square method is given by $y = a + bx$ such that $\sum x = 0$, $\sum y = 84$, $\sum xy = 108$, $\sum x^2 = 70$ for 6 observation at are:

For the given five values $16, 25, 19, 34, 46$, the three years moving averages are

The sale of ice creams is higher in summer than in winter is an example of

Consider the following data: | Year (X) | 2004 | 2005 | 2006 | 2007 | 2008 | 2009 | 2010 | |---|---|---|---|---|---|---|---| | Profit (₹) (y) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | The equation of straight line trend by using least square method is $y = 138.86 + 7.64 (x - 2007)$, then the trend values for the year 2004 is

The behavior and pattern of the data in a time series is NOT based on which of the following component?

Let $y = 138.86 + 7.64(x - 2021)$ be a straight line of best fit by using least square method to the following data: | Year(x) | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | 2024 | |---|---|---|---|---|---|---|---| | Profit(y) (in Rs. '000) | 114 | 130 | 126 | 144 | 138 | 156 | 164 | Then the trend value for the year 2024 is:

For the given five values, 13, 17, 21, 22, 32; the 3-year moving averages are:

In a time series, the variations which occur due to general tendency of the data to increase or decrease over a long term are known as:

If $(t_1, y_1), (t_2, y_2), (t_3, y_3), ..., (t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t)$, the sum of the deviations of y from their corresponding trend value is equal to:

The rise and fall of share market is an example of

If for the following data: | Year (x) | 2000 | 2001 | 2002 | 2003 | 2004 | 2005 | 2006 | |---|---|---|---|---|---|---|---| | Production(in tonnes) (y) | 40 | 45 | 46 | 42 | 47 | 50 | 46 | the equation of the straight line trend is $y = 45.143 + 1.036(x - 2003)$, then the trend value for the year 2004 is

For the given five values 18, 25, 20, 36, 49, the three years moving averages are

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 five values, 15, 24, 18, 33, 42, the three-year moving averages are

Which of the following are examples of irregular trends in a time series? (A) Decrease in production due to a sudden strike. (B) The rise in prices before festivals (C) Unusual rise in income of the printing press due to the announcement of an election. (D) Fall in crop yield due to floods. Choose the correct answer from the options given below:

Which of the following are normal equations to fit a straight line trend y = a + bx by the method of least squares?

The following data shows the percentage of rural and urban Indian households who have a high speed internet connection. | Year (x) | Rural Household (y%) | Urban Household (y%) | |---|---|---| | 2020 | 2 | 6 | | 2021 | 3 | 7 | | 2022 | 3 | 9 | | 2023 | 4 | 15 | | 2024 | 5 | 20 | Based on the above data, which of the following statements are correct? (A) A straight line trend by the method of the least squares for rural Indians is $y^t$ = 3.4 + 0.7 (x - 2022) (B) A straight line trend by the method of the least squares for urban Indians is $y^t$ = 11.4 + 4.3 (x - 2022) (C) The forecast for the year 2025 for urban group using the trend equation is 22.2 %. (D) The forecast for the year 2025 for rural group using the trend equation is 5.5 %. Choose the correct answer from the options given below:

Irregular trends in a time series are caused by (A) Epidemics (B) Strikes (C) Festival season (D) Floods Choose the correct answer from the options given below:

In an influenza epidemic, the number of cases diagnosed in a week were as follows: | Day | Monday | Tuesday | Wednesday | Thursday | Friday | Saturday | Sunday | |---|---|---|---|---|---|---|---| | Number of Cases | 10 | 12 | 8 | 16 | 9 | 14 | 4 | The 3-day moving averages are:

| Year (x) | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | 2017 | |---|---|---|---|---|---|---|---| | Sales (in lakh Rs.) (y) | 65 | 68 | 70 | 72 | 75 | 67 | 73 | If $y = 70 + 0.964(x - 2014)$ be a straight line trend fitted by the method of the least squares to the above data, then the trend value for the year 2015 is:

The pattern and behavior of the data in any time series are based on which of the following components: (A) Secular trend component (B) Seasonal component (C) Cyclical component (D) Irregular component Choose the correct answer from the options given below:

The number of letters posted in a certain city on each day for a week is given as follows: 40, 55, 28, 25, 31, 52, 43. Which of the following is not an entry in the three-day moving averages?

| Year (t) | 2010 | 2011 | 2012 | 2013 | 2014 | 2015 | 2016 | |---|---|---|---|---|---|---|---| | Sales (in Rs. crores) (y) | 6 | 8 | 9 | 11 | 13 | 17 | 20 | In reference to the above data, which of the following statements are correct? (where $x = t - 2013$) (A) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2017 is 21.16. (B) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2013 is 11. (C) If the equation of the straight line trend is $y = 12 + 2.29 x$, then the trend value for the year 2015 is 17. (D) If $(t_1, y_2),(t_2, y_2),(t_3, y_3),......,(t_n, y_n)$ denote the time series and $y_t$ are the trend values of the variable y, then $\sum(y - y_t) = 0$. Choose the correct answer from the options given below:

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?

The rise in prices before festivals is an example of

For the given 5 values 24, 18, 33, 42, 24; the 3-year moving averages are:

Due to which of the following, the irregular variations in a time series are caused: (A) Floods (B) Rise in prices before festivals (C) A fire in a factory (D) Epidemics Choose the **correct** answer from the options given below:

Which of the following are the components of a time series? (A) Cyclic component (B) Regular component (C) Seasonal component (D) Economic component Choose the **correct** answer from the options given below:

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:

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. (C) Time series helps to plan future operations. (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:

Which of the following is not a component of the time series?

For the given 5 values, 15, 18, 21, 27,39; the three year moving averages are:

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

On which of the following components, the pattern and behavior of the data in any time series is based? (A). Secular trend component (B). Seasonal component (C). Cyclical component (D). Regular component Choose the correct answer from the options given below:

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

Which of the following statements are correct? (A) The method of least squares determines the position of the trend line of the given time series. (B) The trend line is called the line of best fit. (C) The line of best fit is a line in which the sum of deviations of the actual values of the variable from their corresponding trend value is always positive. (D) The normal equations of the trend line $y = a + bx$ are $\sum y = na + b \sum x$ and $\sum xy = a \sum x + b \sum x^2$, where $n$ is the numbers of observations. Choose the *correct* answer from the options given below:

If $y = 38.85 + 7.64(x - 2020)$ is the equation of the straight line trend for the following data: | Year $(x)$ | 2017 | 2018 | 2019 | 2020 | 2021 | 2022 | 2023 | |---|---|---|---|---|---|---|---| | Profit (Rs. '000) $(y)$ | 14 | 30 | 26 | 44 | 38 | 56 | 64 | The trend value for the year 2021 by least square method is:

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?

In the month of January, the number of cases diagnosed of influenza epidemic are given in the following table | Date | 1 | 2 | 3 | 4 | 5 | 6 | 7 | |---|---|---|---|---|---|---|---| | Number of cases | 2 | 0 | 5 | 12 | 20 | 27 | 46 | The 3-day moving averages are:

For the given five values $12,15,18,24,36$; the three-year moving averages are :

Which of the following are components of a time series ? (A) Irregular component (B) Cyclical component (C) Chronological Component (D) Trend Component Choose the <b>correct</b> answer from the options given below :