Visit us online at ca.gr2math.com ISBN: 978-0-02-111966-0 MHID: 0-02-111966-X Homework Practice and Problem-Solving Practice Workbook Contents Include:. 120 Homework Practice worksheets. Extra Examples Extra Examples shows you additional worked-out examples that mimic the ones in your book. These page links are in Rich Text Format (rtf.). The Year 8 Interactive Maths software is compatible with both Windows® and Mac® computers. Discover more about Year 8 Interactive Maths. Viewing the 17 chapter screen shots shown below that show step-by-step solutions in G S Rehill's proven writing style. Inventory, chapter, unit, and final tests in this Assessment Guide provide a snapshot of the content that the student has mastered. These tests are available in multiple.
Statistics for Economics Class 11 NCERT Solutions Chapter 2 Collection of Data
Question 1.
Frame at least four appropriate multiple choice options for following questions
(i) Which of the following is the most important when you buy a new dress?
(ii) How often do you use computers?
(iii) Which of the newspapers do you read regularly?
(iv) Rise in the price of petrol is justified.
(v) What is the monthly income of your family?
Answer:
(i) Which of the following is the most important when you buy a new dress?
- Price of the dress
- Fabric of the dress
- Colour of the dress
- Brand of the dress
(ii) How often do you use computers?
- At least once a day
- At least once a week
- At least once in fortnight
- Occasionally
(iii) Which of the newspapers do you read regularly?
- Times of India
- Hindustan Times
- Indian Express
- The Hindu
(iv) Rise in the price of petrol is justified.
- Strongly agree
- Strongly disagree
- Neither agree nor disagree
- Somewhat agree
(v) What is the monthly income of your family?
- Less than ₹ 10,000
- More than ₹ 10,000 but less than ₹ 25,000
- More than ₹ 25,000 but less than ₹ 50,000
- More than ₹ 50,000
Question 2.
Frame five two-way questions (with Tes’ or ‘No’).
Answer:
- Are you an Indian? (Yes/No)
- Do you live in Delhi? (Yes/No)
- Are you graduate? (Yes/No)
- Do you know swimming? (Yes/No)
- Have you ever been convicted by a court of law? (Yes/No)
Question 3.
State whether the following statement are true or false.
(i) There are many sources of data. (True/False)
Answer:
False
There are mainly two sources of data : Primary and Secondary.
(ii) Telephone survey is the most suitable method of collecting data, when the population is literate and spread over a large area. (True/False)
Answer:
False
Mailing questionnaires would be more suitable as the population is literate. Telephonic survey is most suitable in case of illiterate population spread over a large area.
(iii) Data collected by investigator is called the secondary data. (True/False)
Answer:
False
Investigator may collect the data by conducting an enquiry or an investigation. Such data are called primary data, as they are based on first hand information.
(iv) There is a certain bias involved in the non-random selection of samples. (True/False)
Answer:
True
In a non-random sampling method all the units of the population do not have an equal chance of being selected and convenience or judgement of the investigator may create a bias.
(v) Non-sampling errors can be minimised by taking large samples. (True/False)
Answer:
False
It is difficult to minimise non-sampling error even by taking a large sample as they include Errors in Data Acquisition, Non-Response Errors and Sampling bias.
Question 4.
What do you think about the following questions. Do you find any problem with these questions? If yes, how?
(i) How far do you live from the closest market?
Answer:
This question is ambiguous people will not be able to answer this question as the different measures of distance like meters, kilometers, yards etc will complicate the analysis. It should be made specific as Flow many kilometers away is your home from the closest market?
- Less than 5 km
- Between 5-10 km
- More than 10 km
(ii) If plastic bags are only 5 per cent of our garbage, should it be banned?
Answer:
This question is a leading question, which gives a clue about how the respondent should answer by trying to point that 5% is a small percentage which can be tolerated. Better question would be Do you think plastic bags should be banned? (Yes)
(iii) Wouldn’t you be opposed to increase in price of petrol?
Answer:
This question comprises of two negatives which creates confusion to the respondents and may lead to biased response. Better question would be Would you opposed the increase in price of petrol?
(iv)
(a) Do you agree with the use of chemical fertilizers?
(b) Do you use fertilizers in your fields?
(c) What is the yield per hectare in your field?
Answer:
The order or sequence of questions is incorrect. The series of questions should move from general to specific. The correct order would be
(a) What is the yield per hectare in your field?
(b) Do you use fertilizers in your fields?
(c) Do you agree with the use of chemical fertilizers?
Question 5.
You want to research on the popularity of vegetable atta noodles among children. Design a suitable questionnaire for collecting this information.
Answer:
Questionnaire
Name ………………………………….
Age …………………………………………
Address …………………………………
……………………………………………….
………………………………………………
Gender: Male □ Female □
Question 1.
Do you eat noodles?
(a) Yes □
(b) No □
Question 2.
Do you like noodles more than other snacks?
(a) Yes □
(b) No □
Question 3.
How many packets do you consume in a month?
(a) Less than 2 packets □
(b) 3-5 packets □
(c) 5-8 packets □
(d) More than 8 packets □
Question 4.
Do you prefer atta noodles over maida noodles?
(a) Yes □
(b) No □
Question 5.
Do you like vegetables in your noodles?
(a) Yes □
(b) No □
Question 6.
Do you think more vegetables should be added in vegetable atta noodles?
(a) Yes □
(b) No □
Question 7.
Which vegetables according to you should be added in vegetable atta noodles?
…………………………………………………
Question 8.
Do you think it should be spicier?
(a) Yes □
(b) No □
Question 9.
When do you prefer to have vegetable atta noodles?
(a) In breakfast □
(b) In lunch □
(c) As evening snacks □
(d) In dinner □
Question 10.
Do your parents also like vegetable atta noodles?
(a) Yes □
(b) No □
Question 6.
In a village of 200 farms, a study was conducted to find the cropping pattern. Out of the 50 farms surveyed, 50% grew only wheat. Identify the population and the sample here.
Answer:
The population or the Universe in statistics means totality of the items under study. It is a group to which the results of the study are intended to apply. In this case, the population is 200 farms in the village.
A sample refers to a group or section of the population from which information is to be obtained. A good sample (representative sample) is generally smaller than the population and is capable of providing reasonably accurate information about the population. In this case, the sample is 50 farms which are surveyed.
Question 7.
Give two examples each of sample, population and variable.
Answer:
Example 1 A study was conducted to know the average weight of students of class seventh in Delhi. The total number of students in class seventh was 2860. Out of these 200 students were randomly selected and their weight was recorded.
In this example
- Population is, the no of students of class seventh in Delhi, the total number of which is equal to 2860.
- Sample is, the 200 students selected whose weight was recorded.
- Variable under study, is the weight of the students.
Example 2 A person suffering from weakness and fatigue was advised by the doctor to have his blood test done for detection of anaemia. The pathologist took 2 ml of his blood for the test and tested the haemoglobin level in the blood.
In this example
- Population is the total amount of blood in the person’s body.
- Sample is, the 2 ml blood tested.
- Variable under study, is the haemoglobin in the blood sample.
Question 8.
Which of the following methods give better results and why?
(a) Census
(b) Sample
Answer:
(b) In terms of accuracy of results, census is better as it studies all the units of population but this method is very time consuming, expensive and sometimes not feasible to use. Hence, sampling is better due to following reasons
- Economical Sampling involves study, of a fraction of population and hence the cost involved In sampling is relatively low.
- Time Saving Huge amount of time is required to conduct a census survey while sample studies do not take that much time.
- Lesser Effort As only a part of the population is studied, it entails lesser effort on the part of the investigator than that required in census.
- Considerable Accuracy Results from sampling may not be as accurate as in case of sampling but the level of accuracy of these results can be established through statistical tests of significance and hence can be applied in general to the whole population if found significant.
Question 9.
Which of the following errors is more serious and why?
(a) Sampling error
(b) Non-sampling error
Answer:
(b) Sampling error refers to the difference between the sample estimate and the actual value of a population characteristic. This type of error occurs when one makes an observation from the sample taken from the population. It is possible to reduce the magnitude of sampling error by taking a larger sample.
Non-sampling errors are more serious than sampling errors because a sampling error can be minimised by taking a larger sample but it is difficult to minimise non-sampling error, even by taking a large sample. Even a Census can contain non-sampling errors. These include errors in data acquisition, non-response errors and sampling bias.
Question 10.
Suppose there are 10 students in your class. You want to select three out of them. How many samples are possible?
Answer:
In general, you use combinations to determine the number of ways you can select a sample of size n from a population of size N. The formula for the number of such combinations is
N! (n!) (N – n)!
where N! (spoken “Nfactorial”) equals N(N — 1)(N – 2)…(3)(2)(1)
(e.g., 5! = (5) (4) (3) (2) (1) = 120
In this problem, our population size is N = 10 students, and our sample size is n = 3 students. Number of samples possible can be calculated as follows
Number of samples = 10! (3!) (10 – 3)!
= 10!(3)!(7)! = (frac{10 times 9 times 8 times 7 !}{3 times 2 times 1 times 7 !})
= 120 possible random samples
Question 11.
Discuss how you would use the lottery method to select 3 students out of 10 in your class?
Answer:
A representative (random) sample of 3 students can be taken out of 10 through lottery method. The names of all the 10 students of the class are written on 10 separate pieces of paper of equal size and all the slips are folded in a similar manner. These slips are then mixed well and 3 slips with these names are selected one by one so that all the students have equal chance of being selected in the sample.
Question 12.
Does the lottery method always give you a random sample? Explain.
Answer:
Lottery method always gives a random sample if it is used in the proper manner without any bias. If the slips are prepared properly and drawn out one by one so that all the slips have equal chance of being selected in the sample, it will definitely give a random sample. But, if the slips are not mac . of identical size and identification is possible of the names or numbers on the slips, the selection will become biased.
Similarly, if the same name or number is written on more than one slip and if some name or number is missed then also the chances of selection of different units of population in the sample will not be equal. In such cases even lottery method will not give random sample.
Question 13.
Explain the procedure of selecting a random sample of 3 students out of 10 in your class, by using random number tables.
Answer:
Random number tables have been devised to guarantee equal probability of selection of every individual unit in the population according to their listed serial number in the sampling frame. They are available either in a published form or can be generated by using appropriate software packages.
The procedure of selecting a random sample of 3 students out of 10 in a class, by using random number tables is as follows
- Assign a specific number between 1 and 10 to all the 10 students.
- Here, the largest serial number is 10 which is a two digit number and therefore we consult two digit random numbers in sequence.
- We can start using the table from anywhere, i.e., from any page, column, row or point and select the first number randomly. We need to select a sample of 3 students out of 10 total students.
- We will select two more numbers from the table according to sequence. We will skip the random numbers greater than 10 since there is no student number greater than 10. Thus, the 3 selected students are with serial numbers.
Question 14.
Do samples provide better results than surveys? Give reasons for your answer.
Answer:
A survey, which includes every element of the population, is known as Census or the Method of Complete Enumeration. On the other hand, when a part of the population is studied and predictions are made about the population based on this part, it is called sampling.
In terms of accuracy of results, census is better as it studies all the units of population but this method is very time consuming, expensive and sometimes not feasible to use. Hence, sampling is better due to following reasons
- Economical Sampling involves study of a fraction of population and hence the cost involved in sampling is relatively low. Census costs are high especially in case of large population with wide coverage in terms of area.
- Time Saving Huge amount of time is required to conduct a census survey if the population size is large or spread over a wide area while sample studies do not take that much time to be conducted.
- Lesser Effort As only a part of the population is studied, it entails lesser effort on the part of the investigator than that required in census.
- Inappropriateness of Census In certain case, when the population is infinite or exhaustible, census cannot be done and hence sampling is the only choice, e.g., one cannot burn all the units of coal available to know their calorific value; sample is the only means of testing it.
- Considerable Accuracy Results from sampling may not be as accurate as in case of sampling but the level of accuracy of these results can be established through statistical tests of significance and hence can be applied in general to the whole population if found significant.
Statistics for Economics Class 11 NCERT Solutions
NCERT Solutions for Class 11 Economics
NCERT Solutions for Class 5 Maths Math Magic : Class 5 in many is considered as the base for many subjects. This is the standard in which many topics are introduced for the first time. These topics will be useful in advanced classes later on. One of this subject that requires a student to have a strong base is maths. Thus, we are bringing CBSE 5th class maths textbook solutions of math magic, that can help students find the solutions to the exercises and thereby have a better understanding of the subject.
NCERT Solutions for Class 5 Maths Math Magic
NCERT Solutions for Class 5 Maths Math Magic Workbook Pdf, Worksheets, Notes, Questions and Answers.
In CBSE class 5 maths textbook, students will basic maths topics like factors, large numbers, HCF and LCM, fractions, divisibility tests, decimals, averages, profit and loss, and many more. Thus, NCERT 5th class maths book solutions becomes a very important article for the students who are seeking help on these topics. In this article, we are helping you with the overview of each chapter given in the NCERT textbook.
Class 5 Maths Chapter 1 The Fish Tale
Some of the major topics that students are going to study in this chapter are calculating the distance traveled by boat with the help of distance and calculating the money boats that are made by selling prawns and fish. Furthermore, students will learn about the multiplication rule of calculating the overall fishes that are caught.
Class 5 Maths Chapter 2 Shapes and Angles
In this chapter, various angles and shapes are explained in a very interactive manner. This will be explained to students using 3D models, interesting pictures, videos, and images. Along with students will be taught how to calculate the angle between the hand and the arm in the clock? What is the angle formed between the abdomen and a thigh? What will be the angle made by the hands of a clock when the time at 1040 pm? These are the types of questions that students will be able to solve after understanding this chapter.
Class 5 Maths Chapter 3 How Many Squares
This chapter will give you a reference about the rectangles. There are various types of examples and solutions given in this chapter. Which of the given rectangle has the longest perimeter? When dots are given, how many rectangles can be formed? These are some of the questions that will be answered in this chapter.
Class 5 Maths Chapter 4 Parts and Whole
There are different types of examples related to parts and whole are given in this chapter. Some of the examples are as follows, Raj had chocolate. Of which he gave 1/3 rd to Soham, 1/4th to Raju, and 1/6th to Shrey. Raj ate the remaining chocolate. Find the number of pieces that each person got. The other example is the various shapes that are used for the area models. Furthermore, you will be asked to mark some squares in a grid. Then you will be asked about the part that you have marked. Also, the final part that remains marked needs to be answered.
Class 5 Maths Chapter 5 Does it Look the Same?
NCERT solutions for class 5 maths is designed in such a way that patterns and shapes are discussed in a way which students can understand. The solutions given here are step by step guide along with the tips and tricks that make the learning process easier. There are many different concepts that are covered in this chapter. Some of them are preparing various types of patterns and then identifying them. Changing the way and position of alphabet figures and also comparing them. Learning different shapes of various patterns given in the chapter.
Class 5 Maths Chapter 6 Multiple, I’ll be Your Factor
In this chapter, students will learn about jumping and skipping 2 or 3 numbers and thus forming a series using it. Figuring out the numbers that are divided by 2, 3, or 4. Also, you will be explained various multiples of a number given in the sequence. Furthermore, you will be asked to find out the smallest common factors and much more.
Class 5 Maths Chapter 7 Can You See The Pattern
Chapter 7 of the NCERT textbook comprises of can you see the pattern. This chapter helps students in understanding various shapes and patterns. The solutions given in the chapter 7 of class 5 maths contains examples like filling the square using only the numbers from 46 to 54. Also, the rule is that the total for each line should not be more than 120.
Class 5 Maths Chapter 8 Mapping Your Way
NCERT solutions for class 5 maths has different types of many problems and examples that show various types of questions that can be asked in the exam. In this chapter, some of the major questions that can be asked find the distance of the landmark that is more closer to river or building, in comparison with other find out the area of an object when it’s size is reduced, identify the shape given in the figure and picture and how many sides are there, etc. These are some of the examples that you will get to solve in this chapter.
Class 5 Maths Chapter 9 Boxes and Sketches
This chapter in the NCERT textbook is explained using 3D images, animated videos, and models. Thus, it makes sure that kids can understand the concepts very easily. Also, there are assignments in chapter 9 along with the worksheets for practice. In this chapter, there are many different examples which can be solved by students for practice. The topics discussed in this topic includes finding the shape of boxes using the figure of an open box. You need to figure out which figure can be used to form a box.
Class 5 Maths Chapter 10 Tenths and Hundredths
This chapter 10 of NCERT textbook helps students in understanding and comparing the two figures with given examples. In this chapter, students will find questions related to measuring the length of the tail in the animals. There are examples in questions such as the line that is longest among the given two and length of a 100 rupee note that can help students in understanding this chapter better.
Class 5 Maths Chapter 11 Area and its Boundary
This chapter deals area and boundary, calculating the various areas of squares and rectangles, then the difference between area and length and how to measure these. In this chapter, students are often encouraged to use the basic formulas to find the problems and their solutions. There are also other techniques like multiplying and counting tiles which are also discussed in this chapter. Some of the examples in this chapter that are discussed are what is perimeter, find the area of different rectangles, why does other person have different sizes of belts, etc.
Class 5 Maths Chapter 12 Smart Charts
Chapter 2: Fractions And Decimalsmr. Mac's Page Printable
Diagrams and charts are generally used to express the data visually. These are very easy to represent and also has a lasting impression on students. The information here also is processed faster and quicker. In this chapter, the students are exposed to the information that can easily represent in the form of tables. These are also used to represent the tables and solve problems using that and thus deduce various conclusions.
Class 5 Maths Chapter 13 Ways to Divide and Multiply
This chapter specifically deals with various concepts of division and multiplication. These are two very important concepts from the perspectives of academic as well as non-academic. Furthermore, the questions given in this chapter are moreover related to real-life scenarios.
Class 5 Maths Chapter 14 How Big How Heavy
Chapter 2: Fractions And Decimalsmr. Mac's Page Sheet
In this chapter, students will be taught different methods and units for weighing and measurements. There are different questions related volumes and areas in this chapter. The questions will be moreover related to different concepts that depict real-life situations.
Chapter 2: Fractions And Decimalsmr. Mac's Page Key
NCERT solutions for class 5 maths Math Magic textbook can be a handy tool for students. They can go through the article or download the PDF and solve each chapter one by one.