GSEB Class 12 Statistics Solutions Chapter 4 Time Series Exercise 4.1

Gseb Solutions Class 12 Statistics Part 1 Chapter 4 Time Series Ex 4.1

Gujarat Board Textbook Solutions Class 12 Statistics Part 1 Chapter 4 Time Series Ex 4.1

Question 1. The information about the capacity (in lakh tons) to load ships at a port each year is given below. Find the linear trend using graphical method.

Year	2008	2009	2010	2011	2012	2013	2014	2015
Capacity (lakh tons) y	90	97	108	111	127	148	169	200

Answer: For this problem, the time unit is years, and 'y' represents the capacity. The years range from 2008 to 2015. If we set the origin (starting point) for 't' at the year 2007, the time series data can be shown in the table below.

Time t	1	2	3	4	5	6	7	8
Capacity (lakh tons) y	90	97	108	111	127	148	169	200

We plot the 't' values on the X-axis and 'y' values on the Y-axis, creating points like (1, 90) up to (8, 200) on a graph. Connecting these points with straight lines draws the curve for the given time series.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक ग्राफ दिखाता है जहाँ X-अक्ष पर 'समय' और Y-अक्ष पर 'क्षमता (लाख टन)' है। इसमें दो रेखाएँ हैं: एक 'मूल श्रृंखला' जो दिए गए डेटा बिंदुओं को जोड़ती है, और दूसरी 'प्रवृत्ति' रेखा जो इन बिंदुओं के करीब से गुजरती है और समय के साथ क्षमता में बदलाव का रुझान दिखाती है।In simple words: This method helps us see the pattern of ship loading capacity over years by drawing a line on a graph that shows if it is going up or down.

🎯 Exam Tip: Focus on accurately plotting data points and drawing a clear trend line to represent the overall movement of the series for full marks.

Question 2. The number of tourists (in thousand) visiting a certain tourist place is as follows. Find the trend using a suitable graph.

Year	2010	2011	2012	2013	2014	2015	2016
No. of tourists (thousand)	5	7	10	14	30	41	50

Answer: In this problem, the time unit is years, and 'y' represents the number of tourists. The years cover from 2010 to 2016. By setting the origin for 't' at 2009, the time series data is presented in the following table.

Time t	1	2	3	4	5	6	7
No. of tourists ('000) y	5	7	10	14	30	41	50

The 't' values are plotted on the X-axis and 'y' values on the Y-axis. This creates points like (1, 5) up to (7, 50) on the graph. Connecting these points with straight lines forms the curve of the given time series.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र पर्यटकों की संख्या का ग्राफ दिखाता है, जहाँ X-अक्ष पर 'समय' और Y-अक्ष पर 'हजारों में पर्यटकों की संख्या' है। ग्राफ में 'मूल श्रृंखला' के बिंदु और उन्हें जोड़ती एक रेखा दिखाई गई है। 'प्रवृत्ति' रेखा इन बिंदुओं के करीब से गुजरती हुई पर्यटकों की संख्या में समय के साथ होने वाले बदलाव का रुझान दर्शाती है।In simple words: Plotting the number of tourists each year on a graph helps us see how tourism is changing over time, whether it's growing or declining.

🎯 Exam Tip: Ensure correct scaling on both axes and precise plotting of tourist data points to accurately illustrate the trend.

Question 3. The data regarding number of girls (yt) per 1000 boys in the age group 0-6 years of a state are given in the following table. Obtain the linear trend using graphical method.

Year	1961	1971	1981	1991	2001	2011
Yt	956	948	947	928	883	890

Answer: For this data, the time unit is years, and 'y' (or 'yt') shows the count of girls per 1000 boys. The years included are from 1961 to 2011. If we set the origin for 't' at 1951 and use a scale where each unit represents 10 years, the time series data looks like this:

Time \( t = \frac{\text{year}-1951}{10} \)	1	2	3	4	5	6
No. of girls y	956	948	947	928	883	890

We plot 't' values on the X-axis and 'y' values on the Y-axis. This forms points such as (1, 956) up to (6, 890) on the graph. When these points are connected with straight lines, we get the curve for this time series.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह ग्राफ 0-6 वर्ष की आयु वर्ग में प्रति 1000 लड़कों पर लड़कियों की संख्या का रुझान दिखाता है। X-अक्ष पर 'समय' (10 साल के पैमाने पर) और Y-अक्ष पर 'लड़कियों की संख्या' है। 'मूल श्रृंखला' बिंदुओं को जोड़ती है, जबकि 'प्रवृत्ति' रेखा इन बिंदुओं के करीब से गुजरती है और समय के साथ लड़कियों की संख्या के पैटर्न को दर्शाती है।In simple words: By graphing the number of girls per 1000 boys over many years, we can see if this ratio has been going up or down.

🎯 Exam Tip: Pay attention to the scaling factor for the time axis (e.g., 10-year intervals) as it's crucial for correct plotting and trend analysis.

Question 4. The data about the closing prices of shares of a company for 10 days are given in the following table. Obtain the trend using graphical method.

Day	1	2	3	4	5	6	7	8	9	10
Price of share (Rs.)	297	300	304	299	324	320	318	324	329	328

Answer: In this case, the time unit is days, and 'y' represents the share price. The variable 't' takes values from 1 to 10. The time series data is presented in the table below.

Time t	1	2	3	4	5	6	7	8	9	10
Price of share (Rs.) y	297	300	304	299	324	320	318	324	329	328

We plot 't' values on the X-axis and 'y' values on the Y-axis. This creates points like (1, 297) up to (10, 328) on the graph. Connecting these points with straight lines creates the curve for this time series.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह ग्राफ एक कंपनी के शेयर की समापन कीमतों का रुझान दर्शाता है। X-अक्ष पर 'समय' (दिनों में) और Y-अक्ष पर 'शेयर की कीमत' है। 'मूल श्रृंखला' के बिंदु दिए गए डेटा को दर्शाते हैं। 'प्रवृत्ति' रेखा इन बिंदुओं के करीब से गुजरती है और शेयर की कीमत में समय के साथ होने वाले बदलाव का रुझान दिखाती है।In simple words: By plotting a company's daily share prices on a graph, we can see the general direction the share price is moving, whether it's increasing or decreasing.

🎯 Exam Tip: Carefully mark each day's closing price and connect them to form the original series, then draw a smooth trend line that represents the overall movement.