Maharashtra Board Class 10 Maths Chapter 6 Statistics Set 6.5 Solutions

Question 1. Observe the following frequency polygon and write the answers of the questions below it.
(i) Which class has the maximum number of students?
(ii) Write the classes having zero frequency.
(iii) What is the class mark of the class, having frequency of 50 students?
(iv) Write the lower and upper class limits of the class whose class mark is 85.
(v) How many students are in the class 80 - 90?
ℹ️ चित्र व्याख्या (Diagram Explanation): यह एक आवृत्ति बहुभुज है जो छात्रों की संख्या और प्राप्त अंकों को दर्शाता है। Y-अक्ष पर 'छात्रों' की संख्या (1 cm = 10 छात्र) और X-अक्ष पर 'अंकों' को (2 cm = 10 अंक) दर्शाया गया है। यह आलेख (35, 20), (45, 40), (55, 50), (65, 60), (75, 35), (85, 15) जैसे बिंदुओं को जोड़कर एक बहुभुज बनाता है।
Answer:
(i) The class 60 - 70 has the maximum number of students.
(ii) The classes 20 - 30 and 90 - 100 have frequency zero.
(iii) The class mark of the class having 50 students is 55.
(iv) The lower and upper class limits of the class having class mark 85 are 80 and 90 respectively.
(v) There are 15 students in the class 80 - 90.
In simple words: This question requires interpreting a given frequency polygon to extract specific information about student distribution across different marks. The answer involves reading coordinates and class intervals directly from the graph.

🎯 Exam Tip: Always clearly label the axes and indicate the scale when drawing frequency polygons, as these are crucial for accurate interpretation and scoring.

Question 2. Show the following data by a frequency polygon.

Answer:

ℹ️ चित्र व्याख्या (Diagram Explanation): यह आरेख एक आवृत्ति बहुभुज है जो परिवारों की संख्या और उनके बिजली बिल को दर्शाता है। Y-अक्ष पर 'परिवारों की संख्या' (1 cm = 50 परिवार) और X-अक्ष पर 'बिजली बिल (Rs.)' को (2 cm = 200 रुपये) दर्शाया गया है। आलेख बिंदुओं (100, 240), (300, 300), (500, 450), (700, 350), (900, 160) और (1100, 0) को जोड़कर बनाया गया है।
In simple words: To draw a frequency polygon from given data, first calculate the class marks for each class. Then, plot points with class marks on the X-axis and corresponding frequencies on the Y-axis. Finally, connect these points with line segments.

🎯 Exam Tip: Remember to calculate the class mark for each class interval (midpoint) before plotting points for a frequency polygon. Also, include an initial and final class with zero frequency to close the polygon on the x-axis.

Question 3. The following table shows the classification of percentages of marks of students and the number of students. Draw a frequency polygon from the table.

Answer:

ℹ️ चित्र व्याख्या (Diagram Explanation): यह छात्रों के अंकों के प्रतिशत और उनकी संख्या को दर्शाता एक आवृत्ति बहुभुज है। Y-अक्ष पर 'छात्रों की संख्या' (1 cm = 5 छात्र) और X-अक्ष पर 'परिणाम (प्रतिशत)' को (1 cm = 10%) दर्शाया गया है। आलेख बिंदुओं (25, 0), (35, 7), (45, 33), (55, 45), (65, 65), (75, 47), (85, 18), (95, 5) और (105, 0) को जोड़कर बनाया गया है।
In simple words: To create a frequency polygon from this data, first determine the class mark for each percentage range. Then, plot points with the class marks on the horizontal axis and the number of students (frequency) on the vertical axis, connecting them with straight lines.

🎯 Exam Tip: Ensure that the frequency polygon starts and ends on the X-axis by including imaginary preceding and succeeding classes with zero frequency. This completes the polygon and represents the entire data range accurately.