GSEB Class 12 Statistics Solutions Chapter 2 Linear Correlation Exercise 2.1

GSEB Solutions Class 12 Statistics Part 1 Chapter 2 Linear Correlation Ex 2.1

 

Question 1. A ball pen making company wants to know the relation between the price (in Rs.) and supply (in thousand units) of its most selling Gel Pen. The following information is collected for it. Draw a scatter diagram and interpret it.

Price (Rs.)	14	16	12	11	15	13	17
Monthly Supply (thousand units)	32	50	20	12	45	30	53

Answer: Let X be the price (in Rs.) and Y be the monthly supply (in thousand units). We plot the given data points: (14, 32), (16, 50), (12, 20), (11, 12), (15, 45), (13, 30), and (17, 53) on a graph. This shows us the scatter diagram.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक स्कैटर डायग्राम दिखाता है जहाँ X-अक्ष पर कीमत (Rs.) और Y-अक्ष पर मासिक आपूर्ति (हज़ार इकाइयों में) दर्शाई गई है। बिंदु विभिन्न कीमतों पर आपूर्ति को दिखाते हैं। स्केल के अनुसार, X-अक्ष पर 1 सेमी = 1 Rs. और Y-अक्ष पर 1 सेमी = 5 हज़ार इकाइयाँ हैं। ये बिंदु बिखरे हुए हैं और एक सीधी रेखा पर नहीं हैं।
From the scatter diagram, we can see that not all points are on a single straight line. The price and supply change in the same direction, meaning they both increase or decrease together, but not by the same amount. So, because the points are not perfectly aligned, there is a partial positive correlation between the pen's price and its supply.
In simple words: When the price of the pen goes up, the supply also tends to go up, but not always in a perfectly straight line. This means they generally move together, showing a connection between price and how much is supplied.

🎯 Exam Tip: When drawing a scatter diagram, ensure your axes are clearly labeled with units and a proper scale is chosen. Accurate plotting of points and a clear interpretation of the correlation (positive, negative, or no correlation, and its strength) are key to scoring full marks.

 

Question 2. A Company manufactures R.O. plants for the factories. The information about the advertisement cost for its sale and the profit from the sale of R.O. plants is given below:

Draw a scatter diagram from this information and state the nature of the relationship between the advertisement cost and profit earned from the sale of R.O. plants.

Advertisement Cost (ten thousand Rs.)	5	6	7	8	9	10	11
Profit (lakh Rs.)	8	7	9	10	13	12	13

Answer: Let X represent the advertisement cost (in ten thousand Rs.) and Y represent the profit (in lakh Rs.). We plot the given data pairs: (5, 8), (6, 7), (7, 9), (8, 10), (9, 13), (10, 12), and (11, 13) on a graph. This creates the scatter diagram.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक स्कैटर डायग्राम दिखाता है जहाँ X-अक्ष पर विज्ञापन लागत (दस हज़ार Rs.) और Y-अक्ष पर लाभ (लाख Rs.) दर्शाया गया है। बिंदु विज्ञापन लागत के मुकाबले लाभ को दिखाते हैं। स्केल के अनुसार, X-अक्ष पर 1 सेमी = 1 इकाई (दस हज़ार Rs.) और Y-अक्ष पर 1 सेमी = 1 इकाई (लाख Rs.) है। ये बिंदु बिखरे हुए हैं और एक सीधी रेखा पर नहीं हैं।
Looking at the scatter diagram, it is clear that the points do not form a single straight line. Both advertisement cost and profit tend to move in the same direction, meaning they generally increase together. However, this change is not always by the same exact amount. Therefore, there is a partial positive correlation between the advertising money spent and the profit earned.
In simple words: When the company spends more on ads, its profits generally go up, but not always by a fixed amount. There's a link between spending on ads and making money.

🎯 Exam Tip: Clearly define the variables X and Y, including their units, before plotting. Pay attention to choosing an appropriate scale for both axes to ensure all data points fit and are clearly visible. A correct interpretation of the scatter, noting both direction and strength of correlation, is essential.

 

Question 3. The following information is collected to study the relationship between the minimum day temperature and sale of woollen clothes during a particular day of winter for six different cities:

Draw a scatter diagram from this information and interpret it.

Minimum day temperature (Celsius)	12	20	8	5	15	24
Sale of woollen clothes (thousand units)	35	10	45	70	20	8

Answer: Let X represent the minimum day temperature in Celsius, and Y represent the sale of woollen clothes in thousand units. We plot the given pairs of data: (12, 35), (20, 10), (8, 45), (5, 70), (15, 20), and (24, 8) on a graph. This results in the scatter diagram.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह चित्र एक स्कैटर डायग्राम दिखाता है जहाँ X-अक्ष पर न्यूनतम दिन का तापमान (सेल्सियस में) और Y-अक्ष पर ऊनी कपड़ों की बिक्री (हज़ार इकाइयों में) दर्शाई गई है। बिंदु विभिन्न तापमानों पर ऊनी कपड़ों की बिक्री को दिखाते हैं। स्केल के अनुसार, X-अक्ष पर 2 सेमी = 5 सेल्सियस और Y-अक्ष पर 1 सेमी = 10 हज़ार इकाइयाँ हैं। ये बिंदु बिखरे हुए हैं और एक सीधी रेखा पर नहीं हैं।
From the scatter diagram, it is evident that not all the plotted points fall on a single straight line. The minimum day temperature and the sale of woollen clothes show changes in opposite directions; for example, as the temperature decreases, sales tend to increase. However, these changes are not in the exact same proportion. Therefore, since the points do not perfectly align, there is a partial negative correlation between the day's minimum temperature and the sales of woollen clothes.
In simple words: When the temperature drops, people buy more woollen clothes, but this connection isn't always perfectly steady. They move in opposite ways, showing a link between cold weather and more sales.

🎯 Exam Tip: When dealing with negative correlation, ensure your interpretation clearly states the inverse relationship between variables. Accurate plotting, clear labeling of axes with correct units, and a precise scale are vital for representing the data correctly and explaining the relationship.