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Xam Idea Class 10 Maths Chapter 14 Solutions: Statistics

Xam Idea Class 10 Maths Solutions Chapter 14 ‘Statistics’ have been created to assist you in solving the questions in this chapter easily. The important topics covered in this chapter are the grouped data, it’s mean and median, and graphical representation of cumulative frequency distribution. These topics carry a high weightage in Class 10 board exams and are also covered in detail in this chapter of Xam Idea solutions.

There are a total of 37 questions in this chapter divided into 6 exercises. These questions are categorized in such a manner that all the sections of the question paper in your school exams are covered thoroughly such as very short and short answer type questions, long answer type questions. The exercises, Higher-order thinking skills (HOTS) and the value-based questions will help you gain complete conceptual clarity in a question-answer format if you solve these exercises extensively using the Instasolv platform as a source of reference. Practising these questions is advised because the exercises in this chapter cover the course in a detailed fashion and are also suitable for quick revision right before your exams.

The Instasolv experts have created this set of solutions to address your doubts simultaneously while solving the questions. Such an approach to aid you in your self-study hours will also help you boost your efficiency of studying. We aim to provide you with a one-stop solution for all your queries related to Chapter 14 ‘Statistics’ in the Xam Idea Class 10 Maths book. These solutions by Instasolv are really insightful for the experienced mentors and will leave you with some practical tips and tricks to approach the word problems correctly. Teaming up with our platform for your self-study will help you achieve a good rank among your batchmates.

Important Topics for Xam Idea Class 10 Maths Solutions Chapter 14: Statistics

Introduction

Any information which is collected in the form of facts and figures for a pre-defined purpose is known as data. The word data comes from the Latin word ‘datum’. The branch of maths that involves the study and extraction of useful information from a given set of data is termed as statistics. The word statistics comes from the Latin word ‘status’ which means ‘a (political) state’ because earlier statistics were used to collect data about the lives of people for policymaking by the State.

In the previous classes, we learnt to organize data in tabulated form and graphical forms such as pictographs, bar graphs, frequency polygons, histograms, etc.

We also learnt to evaluate the three measure of central tendency for a given set of ungrouped data which is summarised as follows:

  • Mean:where f is the respective frequency distribution for a given value of x.
  • Median: when the total number of observations, ‘n’ is an odd number, then.When ‘n’ is an even number, then
  • Mode: The observation that has the highest frequency is termed as the mode.

Grouped Data

The midpoint of a class interval in a given set of grouped data is assumed to have the frequency centred towards itself. This mid-point is also termed as the class mark.

The formula for the class mark of a given class interval can be given as an average of its upper and lower class limits.

Mean of Grouped Data

To find the mean of a given grouped data using the Assumed Mean Method, we will have to follow the steps given below:

  • To find the mean of a grouped data, firstly we find the assumed mean denoted by ‘a’ which is taken to be any value xi among the values x1, x2,…, xn.
  • The second step is to find the difference denoted as di between the progressing value of xi and the assumed mean a, which is termed as the deviation of a from the respective values of xi.

          di = xi – a

  • To find the mean of grouped data, we need to add the mean of the deviations and the assumed mean. Mathematically,

To find the mean using step deviation method, we must proceed according to the following steps:

  • If ‘h’ is the class size of each class interval, then let us assume,

  • Find the mean of ‘ui’ using the following formula,

  • For mean,

Mode of Grouped Data

  • The first step to finding the mode in a grouped data is to identify the modal class of the frequency table. It is the class with maximum frequency.
  • With the help of the modal class, we can now find the mode using the given mathematical formula,such that ‘l’ gives the lower limit of modal class, h denotes the size of the modal class, and f1, f0, f2represent the frequencies of the modal class, preceding class, and the succeeding class respectively.

Median of Grouped Data

To find the median in a given grouped data, we employ the concept of cumulative frequency denoted as cf. The median class is the one in which the cumulative frequency is nearest to. The formula for the median is given as follows,

Such that l gives the lower limit of the median class, n stands for the total number of observations, ‘h’ is the class size, cf is the cumulative frequency of the median class, and f is the frequency of the median class.

Exercise Discussion of  Xam Idea Class 10 Maths Solutions Chapter 14: Statistics

Very Short Answer Type Questions

This exercise consists of questions that will require minimalist answers. These questions are completely based on the formulae for the mean, median, and mode. You will be given with diagrams for aiding clarity in understanding the demand of the question. Some questions covered in this exercise include tricky questions about the mean, median, and mode.

Short Answer Type Questions

There are 2 exercises in this section namely I and II. The questions in this section are word problems based on the measures of the central tendencies of the grouped data using the direct formulae. In some problems, you will be required to display a strong knowledge base in topics such as mean, median, and mode using different methods.

Long Answer Type Questions

This exercise consists of complex problems in which you will get to evaluate the median and mode of given tabulated data. To solve these questions, you will be required in-depth knowledge of the concepts of statistics and graphical questions.

High Order Thinking Skills

In this exercise, there are advanced level questions that will help you build a strong foundational base with respect to the grouped data and frequency to find the important results of mean, median, and mode. You will be required to find the median for the odd number of observations as well.

Value-Based Questions

The questions in this chapter are based on situational word problems such as the population-based questions, research data analysis. Marks of students in a class, etc.

Why Use Xam Idea Class 10 Maths Solutions Chapter 14: Statistics by Instasolv?

  • The question-answers given in this solutions book by Instasolv will clear your concepts of central tendencies in a detailed manner.
  • Our meticulous mentoring team will reduce your time of practice and will enhance your productivity exponentially through a comprehensive step by step guidance.
  • The solutions book by the Instasolv experts provides detailed answers to each question in Chapter 14 of the Xam Idea Class 10 Maths Solutions in an interactive and interesting way.
  • We have explained each answer in compliance with the CBSE guidelines with a compromise in the quality of the solutions.
  • Our team of experts employ simple language to impart a better understanding of the chapter
  • Instasolv aims to provide a one-stop solution for all your queries and hence, our student-friendly platform is to complement these objectives.
  • The solutions will cost you nothing but add value towards your growth by helping you finish your course well in time.