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It can be observed that the difference between two consecutive upper class limits is 2. The class marks with their respective frequencies are obtained as below. Taking the lower class limits on x -axis and their respective cumulative frequencies on y -axis, its ogive can be obtained as follows.
Bar graphs , histograms , and frequency polygons were also explained earlier. In this chapter, the study of three measures namely mean , median and mode from ungrouped data to that of grouped data will be extended. Concept of cumulative frequency , the frequency distribution cumulative and drawing of cumulative frequency curves Ogive is discussed in this chapter.
Firstly, the topic of Mean of Grouped Data is explained. The first solved example is based on the concept of finding the mean of the given data here marks. These types of questions must be solved in tabular form. After that, the upper limit and the lower limit are explained.
It is assumed that the frequency of each class is centered around its midpoint. The direct method is explained with the help of a solved example.
Another method known as the assumed mean method is also explained. After that, Step deviation method to calculate the mean of the given data is explained. Exercise The next section deals with the concept of Mode of grouped data. The class with the maximum frequency is called the modal class. Mode can be equal , less or more than mean. After that students will learn about the Median of Grouped Data. Median can be calculated using the formula and by using the ogive curve.
There is also an important relation between mean, median and mode that can be studied in this chapter. Less than ogive and more than ogive are discussed in this section and how they can be used to find median. Problems of this chapter require more time compared to others thus students need to do a lot of practice to improve their speed and to avoid silly mistakes. Later key points of the chapter are explained in brief.
Page No Question 1: A survey was conducted by a group of students as a part of their environment awareness programme, in which they collected the following data regarding the number of plants in 20 houses in a locality.
Answer: To find the class mark x i for each interval, the following relation is used. Video Solution for statistics Page: , Q. Question 2: Consider the following distribution of daily wages of 50 workers of a factory. Answer: To find the class mark for each interval, the following relation is used. Question 3: The following distribution shows the daily pocket allowance of children of a locality.
Given that, mean pocket allowance, Taking 18 as assured mean a , d i and f i d i are calculated as follows. Question 4: Thirty women were examined in a hospital by a doctor and the number of heart beats per minute were recorded and summarized as follows.
Answer: To find the class mark of each interval x i , the following relation is used. Question 5: In a retail market, fruit vendors were selling mangoes kept in packing boxes. Question 6: The table below shows the daily expenditure on food of 25 households in a locality. Question 7: To find out the concentration of SO 2 in the air in parts per million, i. Answer: To find the class marks for each interval, the following relation is used. Question 8: A class teacher has the following absentee record of 40 students of a class for the whole term.
Answer: To find the class mark of each interval, the following relation is used. Question 9: The following table gives the literacy rate in percentage of 35 cities. Answer: To find the class marks, the following relation is used.
Answer: To find the class marks x i , the following relation is used. Question 3: The following data gives the distribution of total monthly household expenditure of families of a village. To find the class mark, the following relation is used. Question 4: The following distribution gives the state-wise teacher-student ratio in higher secondary schools of India. T have a teacher-student ratio as To find the class marks, the following relation is used.
Question 5: The given distribution shows the number of runs scored by some top batsmen of the world in one-day international cricket matches. Question 6: A student noted the number of cars passing through a spot on a road for periods each of 3 minutes and summarised it in the table given below. Question 1: The following frequency distribution gives the monthly consumption of electricity of 68 consumers of a locality.
Question 2: If the median of the distribution is given below is Answer: The cumulative frequency for the given data is calculated as follows.
Question 3: A life insurance agent found the following data for distribution of ages of policy holders. Answer: Here, class width is not the same. Answer: The given data does not have continuous class intervals.
Continuous class intervals with respective cumulative frequencies can be represented as follows. Length in mm Number or leaves f i Cumulative frequency Answer: Thecumulative frequencies with their respective class intervals are as follows.
Answer: The cumulative frequencies with their respective class intervals are as follows. Question 7: The distribution below gives the weights of 30 students of a class. Question 1: The following distribution gives the daily income of 50 workers of a factory. Answer: The frequency distribution table of less than type is as follows.
Question 2: During the medical check-up of 35 students of a class, their weights were recorded as follows: Weight in kg Number of students Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 Answer: The given cumulative frequency distributions of less than type are Weight in kg upper class limits Number of students cumulative frequency Less than 38 0 Less than 40 3 Less than 42 5 Less than 44 9 Less than 46 14 Less than 48 28 Less than 50 32 Less than 52 Question 3: The following table gives production yield per hectare of wheat of farms of a village.
Answer: The cumulative frequency distribution of more than type can be obtained as follows. Number of houses f i. Daily wages in Rs. Number of workers f i. Daily pocket allowance in Rs. Number of children f i. Number of women f i. Concentration of SO 2 in ppm. Frequency f i. Class mark x i. Number of students f i. Number of cities f i. Number of patients f i. Number of families f i. Number of consumers f i. Number of lamps f i. Number of surnames f i.
Daily income in Rs upper class limits. Weight in kg upper class limits. Number of students cumulative frequency.
The chapter will also help you to study complementary angles by four exercises with 27 questions in total out of which 18 are long and 9 are short. This is a very interesting chapter that will teach you how trigonometry will be used in daily life or around you by calculating the heights and distance of various objects without actually measuring.
The chapter has only one exercise and worth practising. A set of all points in a plain equidistant from a given point is known as a circle. It has two exercises comprises of basic questions in the first and with various equations in the second one.
As the name suggests this chapter has various constructions such as division of line segment and calculations using a ruler and a compass followed by mathematical reasoning against the construction.
The chapter has 2 exercises with 14 long questions. You must have learned in your earlier classes about the methods of finding the perimeter and areas of figures like circles, squares, and rectangles. In this chapter, you will learn about areas related to triangles through exercises of 35 questions in total. In this chapter, you will deal with problems and their solutions to find areas and volumes of various solid objects like cube, cuboid, and cylinders.
This chapter is based on finding mean, median, and mode from ungrouped to grouped data. There will also be questions asked for cumulative frequency distribution and how to dram cumulative frequency curves. There will be a total of 25 long answer questions in 4 different exercises. CBSE follows a step-wise marking scheme, where the students are awarded marks for every correct step performed by them. To test the preparation level of the students, the CBSE brings a slight change in its exam pattern every year.
As a result, all the students must be well aware of the upcoming exam pattern for the Class 10 th Maths exam. Designed by expert educators and curriculum designers, the PDF solutions for Class 10 th Maths are a must for all the students to clear their concepts and perform better in the exams. You do not need to go through all the guides available in the market but effectively practicing and exercising Class 10th NCERT is enough and as the course of CBSE is from NCERT, therefore regular practices will help a student to achieve good marks in maths examinations.
Finding the best and the effective solution for class 10th could be tricky and which is why Swiflearn subject experts have prepared them so that without wasting your time you can start learning right away. The solutions are arranged chapter-wise and exercise-wise so that while practicing without wasting time you can enhance and practice on your CBSE boards. The NCERT provides various study materials textbooks syllabus and also there is a lot of material for teachers as well to prepare the syllabus and the schedule for students preparing for class 10th boards.
The division of the marks is Algebra 20 marks , Trigonometry 12 marks , Statistics, and Probability 11 marks which are easy scoring topics from class 10th board maths marking schemes.
Always practice Trigonometry formulas, Surface Area and Volume formulas, Proving Rational numbers, Long division of polynomials and Algebra Identities are the topics that will help you achieve maximum marks in class 10th mathematics. NCERT Solutions for Class 10 Maths assists all CBSE Class 10 Students in offering some helpful tricks and tips to solve math problems at the end of each chapter and if you are an aspiring maths student or you are looking forward to taking maths after class 10th please clear your concepts with the help of NCERT as these concepts are going to help you in future academic years.
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