Class 10 Maths 1 Statistics Practice Set 6.5 Solutions | Maharashtra Board

Class 10 Maths 1 – Statistics
Practice Set 6.5 Solutions

Introduction

Welcome to Rukmini Classes! In this lesson, we provide the complete solutions to Practice Set 6.5 from Chapter 6, Statistics, of Class 10 Mathematics 1, Maharashtra State Board.

This practice set covers frequency polygons, class-marks, frequencies, and the graphical representation of statistical data.

The solutions are presented in a clear and easy-to-understand format to help students understand the concepts, practise graph drawing, and prepare effectively for the SSC Board Examination.

Learn • Practise • Prepare for Exams

 

Practice Set 6.5 – Solutions

Q.1. Observe the frequency polygon and answer the following questions.

(1) Which class has the maximum number of students?

Answer: The class 60–70 has the maximum number of students, i.e., 60 students.

(2) Write the classes having zero frequency.

Answer: The classes having zero frequency are 20–30 and 90–100.

(3) What is the class-mark of the class having a frequency of 50 students?

Answer: The class-mark is 55.

(4) Write the lower and upper class limits of the class whose class-mark is 85.

Answer:

• Lower class limit = 80
• Upper class limit = 90

(5) How many students are in the class 80–90?

Answer: There are 15 students in the class 80–90.

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

Given data:

Electricity Bill (₹)	Families
0–200	240
200–400	300
400–600	450
600–800	350
800–1000	160

Solution:

Step 1: Calculate the class-marks.

Class-mark = (Lower class limit + Upper class limit) ÷ 2

Class Interval	Class-mark (x)	Frequency (y)
0–200	100	240
200–400	300	300
400–600	500	450
600–800	700	350
800–1000	900	160

Step 2: Plot the points:

(100, 240), (300, 300), (500, 450), (700, 350), (900, 160)

Step 3: Add the zero-frequency points (-100, 0) and (1100, 0) to close the frequency polygon.

Step 4: Join all the plotted points in order using straight lines.

• X-axis: Class-marks of electricity bills
• Y-axis: Number of families

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Q.3. Draw a frequency polygon from the following table.

Result (Percentage)	No. of Students
30–40	7
40–50	33
50–60	45
60–70	65
70–80	47
80–90	18
90–100	5

Solution:

Step 1: Calculate the class-marks.

Class-mark = (Lower class limit + Upper class limit) ÷ 2

Class Interval	Class-mark (x)	Frequency (y)
30–40	35	7
40–50	45	33
50–60	55	45
60–70	65	65
70–80	75	47
80–90	85	18
90–100	95	5

Step 2: Plot the points:

(35, 7), (45, 33), (55, 45), (65, 65), (75, 47), (85, 18), (95, 5)

Step 3: Add the zero-frequency points (25, 0) and (105, 0) to close the polygon.

Step 4: Join all the plotted points in order using straight lines to obtain the frequency polygon.

• X-axis: Class-marks of percentages
• Y-axis: Number of students

Important Note: Choose a suitable scale for each axis while drawing the graphs. Label both axes clearly and join the points using straight lines.