GSEB Class 11 Statistics Solutions Chapter 2 Presentation of Data Exercise 2.3

GSEB Solutions Class 11 Statistics Chapter 2 Presentation Of Data Ex 2.3

 

Question 1. Following is the data on the number of employees working in various Government departments. Present it with a suitable diagram.

Department	Road transport	Railway	Income tax	Finance	Planning
Number of employees	4000	6000	3000	2500	1500

Answer: The departments are positioned on the X-axis, and a scale of 1 cm representing 1000 employees is adopted for the Y-axis. Bars are then drawn for each department to construct a simple bar diagram as illustrated. Since the provided data describes only one variable characteristic-the number of employees across different government departments-a simple bar diagram is the most suitable visual representation for this information.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक साधारण बार चार्ट को दर्शाता है जो विभिन्न सरकारी विभागों में कर्मचारियों की संख्या को प्रस्तुत करता है। क्षैतिज अक्ष (X-axis) पर विभाग (जैसे सड़क परिवहन, रेलवे, आयकर) और ऊर्ध्वाधर अक्ष (Y-axis) पर कर्मचारियों की संख्या दर्शाई गई है, जिसमें 1 सेमी 1000 कर्मचारियों के बराबर है। प्रत्येक विभाग के लिए एक बार की ऊंचाई उस विभाग में कर्मचारियों की संख्या का प्रतिनिधित्व करती है।
In simple words: A simple bar diagram is used to show employee counts in various government departments. Each department gets a bar, with its height indicating the number of employees, following a specific scale.

🎯 Exam Tip: When presenting data for a single variable characteristic, ensure the simple bar diagram is clearly labeled with axes and an appropriate scale for maximum clarity and scoring.

 

Question 2. The data on the profit of a company is as under. Present it by an appropriate diagram.

Year	2010	2011	2012	2013	2014	2015
Profit (in crore Rs.)	10	5	-2	4	8	6

Answer: The given data illustrates the yearly profit of a company, which is a single variable characteristic. Consequently, a simple bar diagram is an appropriate method for its presentation. To construct this diagram, the years are plotted on the X-axis, and the profit (in crore Rs.) is represented on the Y-axis. A scale of 1 cm = 2 crore Rs. profit is used for the bars corresponding to each year, as depicted in the figure.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक साधारण बार चार्ट प्रस्तुत करता है जो विभिन्न वर्षों में एक कंपनी के लाभ (करोड़ रुपये में) को दर्शाता है। क्षैतिज अक्ष (X-axis) पर वर्ष (2010 से 2015) और ऊर्ध्वाधर अक्ष (Y-axis) पर लाभ दर्शाया गया है, जिसमें 1 सेमी 2 करोड़ रुपये के लाभ के बराबर है। प्रत्येक वर्ष के लिए बार की ऊंचाई उस वर्ष के लाभ को इंगित करती है, जिसमें नकारात्मक लाभ भी दिखाया गया है।
In simple words: A simple bar diagram effectively visualizes a company's yearly profit. Years are on the X-axis, profits (in crore Rs.) are on the Y-axis, and bar heights show profit amounts using a 1 cm = 2 crore Rs. scale.

🎯 Exam Tip: When representing profit data, especially with both positive and negative values, ensure the Y-axis scale accommodates the full range, and clearly label units (e.g., "crore Rs.") for accurate interpretation.

 

Question 3. Changes in the price of share of 5 companies at Mumbai Stock Exchange during an interval of 15 days are as follows. Present them by a suitable diagram.

Company	A	B	C	D	E
Price of share (in Rs.)	40	20	100	80	30
Price of same share after 15 days (in Rs.)	60	30	150	60	10

Answer: This dataset involves two distinct variable characteristics: the initial closing price of a share and its closing price after 15 days. Therefore, a multiple bar diagram is the most appropriate visualization method. In this diagram, companies are arranged along the X-axis. The Y-axis represents the share closing prices, using a scale where 1 cm equals Rs. 20. For each company, two bars are drawn side-by-side, representing the two different price points, thus creating a clear multiple bar diagram as shown in the accompanying figure.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक मल्टीपल बार चार्ट है जो मुंबई स्टॉक एक्सचेंज में 5 कंपनियों के शेयरों की कीमतों में 15 दिनों के अंतराल पर हुए बदलाव को दर्शाता है। क्षैतिज अक्ष (X-axis) पर कंपनियों (A, B, C, D, E) और ऊर्ध्वाधर अक्ष (Y-axis) पर शेयर की कीमत (रुपये में) दर्शाई गई है, जिसमें 1 सेमी 20 रुपये के बराबर है। प्रत्येक कंपनी के लिए दो बार हैं - एक प्रारंभिक कीमत के लिए और दूसरा 15 दिनों के बाद की कीमत के लिए, जिससे तुलना स्पष्ट होती है।
In simple words: A multiple bar diagram illustrates share price changes for five companies over 15 days. Companies are on the X-axis, prices on the Y-axis (1 cm = Rs. 20), with two bars per company showing initial and final prices.

🎯 Exam Tip: When comparing two or more related variables across different categories, a multiple bar diagram is ideal. Ensure clear labeling for each bar within a category and use a consistent scale for accurate visual comparison.

 

Question 4. Information regarding the birth rate and death rate of 5 countries is as under. Present it by a suitable diagram.

Country	U.S.A.	Japan	India	Germany	U.K.
Birth rate	16.5	20.8	34.2	16.4	15.2
Death rate	10.2	12.2	20.4	10.3	12.0

Answer: The provided data comprises two distinct variable characteristics: birth rates and death rates for several countries. Consequently, a multiple bar diagram is the most appropriate method for visual representation. In this diagram, the countries are displayed on the X-axis. Both birth rates and death rates are shown on the Y-axis, with a scale of 1 cm representing 5 units. By drawing multiple bars for each country—one for its birth rate and another for its death rate—the diagram effectively illustrates the comparative data as presented in Figure 4.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक मल्टीपल बार चार्ट है जो एक वर्ष के दौरान पांच अलग-अलग देशों की जन्म दर और मृत्यु दर को प्रदर्शित करता है। क्षैतिज अक्ष (X-axis) पर देश (जैसे U.S.A., जापान, भारत) और ऊर्ध्वाधर अक्ष (Y-axis) पर दरें दर्शाई गई हैं, जिसमें 1 सेमी 5 इकाइयों के बराबर है। प्रत्येक देश के लिए, दो बार होते हैं- एक जन्म दर के लिए और दूसरा मृत्यु दर के लिए, जिससे विभिन्न देशों में इन दरों की तुलना आसानी से की जा सकती है।
In simple words: A multiple bar diagram is used to compare birth and death rates across five countries. Countries are on the X-axis, rates on the Y-axis (1 cm = 5 units), with paired bars showing each country's birth and death figures.

🎯 Exam Tip: When visualizing comparative data like birth and death rates across multiple entities, use distinct bar patterns or colors for each variable within the multiple bar diagram to enhance readability and ensure all elements are clearly labeled.

 

Question 5. Information regarding the age of persons living in two different regions is as under. Present it by using an appropriate diagram.

Age	Less than 15 (Child)	15 to 35 (Young)	35 to 60 (Adult)	More than 60 (Old)	Total
Region A	480	360	240	120	1200
Region B	350	250	200	200	1000

Answer: To represent the data on different age groups, a divided bar diagram is constructed. The following table illustrates the calculation of dividing lines for various age sections within each bar:

Age	Area A		Area B
	No. of persons	Dividing line	No. of persons	Dividing line
Less than 15 (Child)	480	1200-480 = 720	350	1000-350 = 650
15 to 35 (Young)	360	720-360 = 360	250	650-250 = 400
35 to 60 (Adult)	240	360-240 = 120	200	400-200 = 200
More than 60 (Old)	120	-	200	-
Total	1200	-	1000	-

In the diagram, Area A and Area B are positioned on the X-axis. The bars are drawn with appropriate width and length, proportional to the number of persons, using a Y-axis scale of 1 cm = 200 persons. This forms a divided bar diagram illustrating the age distribution of individuals across the two areas.
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक विभाजित बार चार्ट है जो दो अलग-अलग क्षेत्रों में व्यक्तियों की आयु के वितरण को दर्शाता है। क्षैतिज अक्ष (X-axis) पर क्षेत्र (Area A और Area B) और ऊर्ध्वाधर अक्ष (Y-axis) पर व्यक्तियों की संख्या (1 सेमी 200 व्यक्तियों के बराबर) दर्शाई गई है। प्रत्येक बार विभिन्न आयु समूहों (बच्चे, युवा, वयस्क, वृद्ध) में विभाजित है, जिससे प्रत्येक क्षेत्र के भीतर आयु संरचना का प्रतिशतिक वितरण स्पष्ट होता है।
In simple words: A divided bar diagram shows age group distribution in two regions. Regions are on the X-axis, population on the Y-axis (1 cm = 200 persons), and each bar is segmented to show proportions of children, young, adults, and old people.

🎯 Exam Tip: When visualizing compositional data for different categories, a divided bar diagram is effective. Ensure each segment within the bar is clearly distinguishable (e.g., by pattern or color) and that the scale accurately represents the total and component values.

 

Question 6. Draw the percentage divided bar diagram for the data given in example 5.

Answer: To construct a percentage divided bar diagram for the data from example 5, a table is first prepared showing the percentages of different age sections relative to the total number of persons in each area, with the total sum normalized to 100 percentage:

Age	Area A		Area B
	No. of persons	Percentage	No. of persons	Percentage
Less than 15 (Child)	480	40	350	35
15 to 35 (Young)	360	30	250	25
35 to 60 (Adult)	240	20	200	20
More than 60 (Old)	120	10	200	20
Total	1200	100	1000	100

The areas (Area A and Area B) are depicted on the X-axis, while the percentages are shown on the Y-axis, with a scale of 1 cm representing 20 percentage points. Bars are drawn for both Area A and Area B with appropriate width and length, normalized to 100 percentage. This results in the percentage divided bar diagram illustrating the age distribution of residents in the two different areas, as follows:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक प्रतिशत विभाजित बार चार्ट है जो दो क्षेत्रों में व्यक्तियों की आयु के प्रतिशत वितरण को प्रदर्शित करता है। क्षैतिज अक्ष (X-axis) पर क्षेत्र (Area A और Area B) और ऊर्ध्वाधर अक्ष (Y-axis) पर प्रतिशत दर्शाया गया है, जिसमें 1 सेमी 20 प्रतिशत के बराबर है। प्रत्येक बार 100% तक पहुंचता है और इसे विभिन्न आयु समूहों (बच्चे, युवा, वयस्क, वृद्ध) में विभाजित किया गया है, जिससे प्रत्येक क्षेत्र के भीतर विभिन्न आयु वर्गों का सापेक्षिक अनुपात स्पष्ट होता है।
In simple words: A percentage divided bar diagram illustrates the proportional age distribution in two regions. The X-axis shows regions, the Y-axis shows percentages (1 cm = 20%), and each bar, totaling 100%, is segmented for different age groups.

🎯 Exam Tip: When using a percentage divided bar diagram, ensure that each bar totals 100% to accurately represent the composition. Use distinct patterns or colors for each category within the bar, and provide a clear legend for easy understanding of the proportions.

 

Question 7. A company has produced the following number of cars during three years. Represent it through a circle diagram.

Year	2012	2013	2014
Production of cars	25,600	1,02,400	1,60,000

Answer: To create a circle diagram for the provided data, we first calculate the square root of the car production for each year. Then, by dividing this square root by 160, we determine the radius for each circle, representing the production for different years. The following table details these calculations:

Year	Production of cars	Square root	Radius (Square root / 160)
2012	25,600	160	\( \frac{160}{160} = 1.0 \)
2013	1,02,400	320	\( \frac{320}{160} = 2.0 \)
2014	1,60,000	400	\( \frac{400}{160} = 2.5 \)

Circles are then drawn with radii corresponding to the car production values for different years, thus forming the circle diagram as follows:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक सर्कल डायग्राम है जो तीन वर्षों (2012, 2013, 2014) में कार उत्पादन को दर्शाता है। प्रत्येक वर्ष के लिए, एक वृत्त खींचा गया है जिसका त्रिज्या उस वर्ष के उत्पादन की मात्रा के वर्गमूल के अनुपात में है (यहाँ, वर्गमूल को 160 से विभाजित करके त्रिज्या प्राप्त की गई है)। यह दृश्य प्रतिनिधित्व विभिन्न वर्षों में उत्पादन के पैमाने को तुलनात्मक रूप से दिखाता है।
In simple words: This circle diagram visualizes car production over three years. Each year has a circle, and its radius is determined by the square root of that year's production divided by 160, illustrating the scale of production.

🎯 Exam Tip: When using circle diagrams to represent magnitudes, ensure the area of the circle (not just the radius) is proportional to the data. If comparing by radius, specify the scaling factor used. Label each circle clearly with the year and its corresponding radius for precise interpretation.

 

Question 8. The following data represent the percentage sales of copies of daily newspapers. Represent it by pie diagram.

Newspaper	P	Q	R	S	Total
Percentage of selling	25	23	24	28	100

Answer: To construct a pie diagram, we first convert the percentage sales of different daily newspapers into degrees, assuming a total sales of 100 percentage corresponds to 360 degrees. The following table shows these calculations:

Daily	Percentage of selling	Degrees	Cumulative degree
P	25	\( \frac{25}{100} \times 360^\circ = 90^\circ \)	\( 90^\circ \)
Q	23	\( \frac{23}{100} \times 360^\circ = 82.8^\circ \)	\( 172.8^\circ \)
R	24	\( \frac{24}{100} \times 360^\circ = 86.4^\circ \)	\( 259.2^\circ \)
S	28	\( \frac{28}{100} \times 360^\circ = 100.8^\circ \)	\( 360.0^\circ \)
Total	100	\( 360^\circ \)	-

Using an appropriate radius, a circle is drawn and then divided into sectors according to the calculated degrees, representing the sales of different daily newspapers. The resulting pie diagram is presented as follows:
ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक पाई चार्ट है जो विभिन्न दैनिक समाचार पत्रों की बिक्री के प्रतिशत वितरण को दर्शाता है। वृत्त को चार सेक्टरों में विभाजित किया गया है, प्रत्येक सेक्टर एक समाचार पत्र (P, Q, R, S) का प्रतिनिधित्व करता है। प्रत्येक सेक्टर का केंद्रीय कोण उस समाचार पत्र की बिक्री के प्रतिशत के सीधे आनुपातिक है, जिससे समग्र बिक्री में प्रत्येक समाचार पत्र का सापेक्षिक हिस्सा स्पष्ट होता है।
In simple words: This pie diagram shows the percentage sales of daily newspapers. A circle is divided into sectors, where each sector's angle corresponds to a newspaper's sales percentage, illustrating its share of the total market.

🎯 Exam Tip: When constructing a pie diagram, ensure that the sum of all percentages is 100% and the sum of all central angles is 360 degrees. Use clear labels or a legend to identify each sector, making the diagram easy to understand and compare proportions.

 

Question 9. Represent the following information by a pictogram:

Year	2010	2011	2012	2013	2014
mangoes (kg)	1,00,000	1,50,000	2,50,000	1,50,000	75,000

Answer: The data on mango production in kilograms from 2010 to 2014 is provided. To create a pictogram for this information, we will use one mango image to represent 50,000 kg of mango production. The pictogram for the given data is prepared as follows:

Year	Production of mango (in kg)
2010	1,00,000 (Two mango images)
2011	1,50,000 (Three mango images)
2012	2,50,000 (Five mango images)
2013	1,50,000 (Three mango images)
2014	75,000 (One and a half mango images)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक पिक्टोग्राम है जो 2010 से 2014 तक आम के उत्पादन (किलोग्राम में) को दर्शाता है। इसमें प्रत्येक वर्ष के आम उत्पादन को आमों के चित्रों की संख्या से दर्शाया गया है, जहाँ एक पूरा आम का चित्र 50,000 किलोग्राम आम का प्रतिनिधित्व करता है। उदाहरण के लिए, 1,00,000 किलोग्राम उत्पादन के लिए दो आम के चित्र और 75,000 किलोग्राम उत्पादन के लिए एक और आधा आम का चित्र उपयोग किया गया है।
In simple words: This pictogram shows mango production from 2010-2014. One mango icon represents 50,000 kg of production; for example, 1,00,000 kg is shown by two mangoes, and 75,000 kg by one and a half mangoes.

🎯 Exam Tip: When creating a pictogram, choose a simple, clear icon and define its value clearly in a key. Ensure the icons are easily countable and represent the data proportionally, using fractions of icons if necessary for accuracy.

 

Question 10. Details of production of electric bulb by two well-known companies are as under. Represent them by a pictogram.

Year	Production of electric bulbs (in lac units)
	Company A	Company B
2012	50	100
2013	100	150
2014	175	200
2015	200	200

Answer: The production data for electric bulbs (in lac units) by two companies, A and B, is provided for the years 2012 to 2015. To represent this information using a pictogram, one bulb image will signify the production of 50 lac electric bulbs. The pictogram illustrating the electric bulb production for Company A and Company B is prepared as follows:

Year	Production of electric bulbs (in lac units)
	Company A	Company B
2012	50 (One bulb image)	100 (Two bulb images)
2013	100 (Two bulb images)	150 (Three bulb images)
2014	175 (Three and a half bulb images)	200 (Four bulb images)
2015	200 (Four bulb images)	200 (Four bulb images)

ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक पिक्टोग्राम है जो 2012 से 2015 तक दो कंपनियों (A और B) द्वारा इलेक्ट्रिक बल्ब के उत्पादन को दर्शाता है। इसमें प्रत्येक कंपनी के वार्षिक उत्पादन को बल्बों के चित्रों की संख्या से दर्शाया गया है, जहाँ एक बल्ब का चित्र 50 लाख इलेक्ट्रिक बल्बों के उत्पादन का प्रतिनिधित्व करता है। उदाहरण के लिए, 50 लाख उत्पादन के लिए एक बल्ब का चित्र और 175 लाख उत्पादन के लिए साढ़े तीन बल्ब के चित्र उपयोग किए गए हैं।
In simple words: This pictogram displays electric bulb production for Companies A and B from 2012-2015. One bulb icon signifies 50 lac units, so 100 lac units are shown by two bulbs, and 175 lac units by three and a half bulbs, allowing visual comparison of production.

🎯 Exam Tip: For pictograms comparing multiple categories or groups (like two companies), ensure consistent icon size and value across all categories. Clearly state the value each icon represents and arrange icons neatly for easy comparison and understanding of relative magnitudes.